Ship Design
Ship design obviously depends a lot on your opponents' and your own development strategy. Many ships which work very well against the computer will fail miserably against a competent human player.
Missile Boats
In the early and middle game, there is no rival to the power of the missile boat. The advantage of a missiles based attack lies in two simple facts:
While ECM, shields, anti-missile rockets, point defense beams, and self-destructing ships can blunt missiles' effectiveness, the computer often fails to use these techniques properly, and in many situations they are not cost-effective and can be overcome with scale.
In the first turns of an average game and occasionally in the beginning stages of pre-warp, a cruiser full of 2-shot plain nuclear missiles can destroy a starbase, so this can make a decent blitz attack against a slow opponent, especially if the attacker is a telepathic race, for which cruisers have special significance. I usually don't try this, since it is not too difficult to thwart this attack with a small amount of research. Reinforced Hull, Heavy Armor, Tritanium Armor, or ECM Jammer will make it next to impossible to kill a starbase with a small fleet. Empty frigates are very difficult to kill with non-FST missiles, so a defender may be able to force a time-limit retreat even if you kill his starbase.
The MIRV option on missiles comes after 2 additional levels of technology, and allows for four warheads in the space of about two. With merculite missile or pollution processor technology, come a decent means of attack, as with the MIRV option the damage density of nuclear missiles is more than doubled. Frigates with MIRV 2-shot nuclear missiles can take out destroyers and some cruisers with titanium armor, and the most cost-effective way to kill space monsters early in the game is the employment of a small fleet of MIRV nuke ships, allowing you to colonize the nice planets you have just liberated in a timely manner. Advanced-tech games against the computer can be won quite reliably by non-creative races who simply refit their existing fleet to contain only MIRV missiles and add an empty frigate. It is not difficult to win a 2-player small-universe game in under 10 turns this way.
Emissions guidance technology (EMG) is often overlooked by those who don't fully understand its function. Any EMG missile damage which is not absorbed by the shield of the target ship is done directly to the engine system, and even the largest ships with the best armor have relatively fragile engines. This technology is essential if you want to kill the Guardian in a reasonable amount of time. EMG can retain its relevance and utility even in the highest technology games, because nothing can come close to it in terms of its ability to annihilate an entire ship while taking a comparatively small amount of space.
Since EMG increases the size of a missile by 300%, it is not cost-effective to use them everywhere, i.e. star bases and planets have no engines, so an EMG missile strike will do the same damage as a normal missile strike, but will cost you much more. In general, it is best to use the modification sparingly and make sure the missile's energy is spent on the engine. This can be accomplished by placing cheap, armored missiles on top of a stack to absorb antimissile fire, and placing MIRVed missiles between the cheap and the EMG missiles if the target is expected to have shields. EMG missiles should always be MIRV if the option is available, since each modification only increases the space and cost by a constant value instead of a percentage.
EMG is primarily blunted by sheilds and point defense, so it works best when attacking ships with no shields from behind. Naturally, the Antareans come to mind. EMG missiles are key to killing the Antarean home fleet in an absolute minimum of time and effort.
A final advantage of missiles over beam weapons arises in planetary bombardment, where beam damage is halved by atmospheric entry. This becomes a major concern when the enemy has decent shields technology. For example, heavy mount lasers do zero damage against a planet whose owner has class III shield technology, since the 6 maximum damage is halved to 3 and 3 is then subtracted by the shield. Nuclear missiles still do 5 damage per warhead, though. If the said planet has a radiation shield, then you need merculites, but even these are much lower-tech than the earliest beam system which can do decent damage to such a planet. MIRV merculite does 24 damage. Hv Gauss Cannon does 6 damage.
Beam Weapons
The earliest effective beam ship uses a combination of AF AP NR lasers and battle scanner. If the lasers are heavy-mounted, you can often dispose of enemy missile boats before they have a chance to fire. However, reinforced hull makes such small ships very annoying. A battleship armed as above is usually the foundation for a reliable telepathic attack against the computer, and it can be launched by turn 60 in pre-warp, given favorable conditions. The "laser boat" has some disadvantages other than those mentioned earlier: If your enemy's fleet has high beam defense (due to mobility from empty space, or racial bonus), then you will not hit often enough to make a quick kill, and your ship will succumb to a few missiles at this stage in the game, since Pd AF lasers aren't too great at shooting down ARM missiles. Also, the computer can make life difficult for you by happening to research reinforced hull or heavy armor, lengthening the time required to kill a starbase by a factor of at least three.
The next cost-effective beam ship design is the mass driver (MD) ship. When you research Class III shield (or radiation shield or warp dissipator), mass drivers get the auto-fire (AF) option, and inertial stabilizer (IS) is on the way to that tech level. A battleship built with Class III shield, IS, and Hv AF MD's is quite a formidable anti-ship design. Also, Pd AF MD's are decent anti-missile weapons, only losing effectiveness with the advent of zortrium armor. Its only weakness (a big weakness) in that time frame is in planetary bombardment. Some try to remedy this deficiency by bringing a few bombs or missiles. If you are attacking a planet with a missile base and/or fighter garrison, it is advisable to have a dedicated point defense ship for eliminating small targets. Enveloping fusion beams arise at about the same tech level as AF MD's, but they are not nearly as nice, because of intermediate tech issues.
Other beams are influential, but do not play as large a role in a fast-paced game. I merely comment that the next truly cost-effective beam weapon is the auto-fire Gauss cannon, for which the AF option is available at the 4500RP level (as opposed to 900RP for AF MD). Beyond Gauss cannon, all of the beam weapons are nice, but require extensive research to miniaturize. Before the patch, plasma cannons were the best weapon in the game, but that has changed, as they have become much more expensive.
Other useful designs
Often you just want to survive a battle long enough for your missiles to reach your targets after your missile ships have retreated, or you want to survive long enough to force a time-limit retreat, if you are feeling cheap. The most primitive solution is the empty frigate, which costs a mere 20 production, and it is surprisingly effective early on, as it can outrun missiles and dodge beams fairly well. This frigate can be further modified by technology such as battle pods, inertial stabilizer, and augmented engines, giving it beam defense close to 200%. If you want serious lasting power, you probably want some shields to regenerate any damage from the rare beam strike (at least 5% chance no matter what), although this may hurt beam defense. However, there is no defense penalty for class I shield on a weaponless frigate with battle pods and augmented engines at the 650 RP level (see the short game referenced above).
Probably the best early implementation of torpedo technology is the "Supreme Truth" battleship, which has about 6 anti-matter torpedoes, battle pods, augmented engines, inertial stabilizer, and a lot of empty space. In combat, this ship should simply run around and throw torpedoes at the enemy, who will have trouble hitting Supreme Truth with any consistency. While this design performs well in one-on-one combat against ships at its tech level, it has a lot of trouble in planetary assault and fleets of missile ships. It cannot outrun the constant stream of missiles from a missile base, and the torpedoes' damage is reduced drastically by a planet's atmosphere. Hence, this is best used as a defensive ship.
Marine action in combat can play a key role in the game: ships captured can be scrapped for technology and money, and raids can destroy a ship without having to do any damage to the structure itself. Since marine action is covered in the section on capturing Antarean ships there is no need to discuss some details, such as the utility of assault shuttles. The other two methods, tractor beams and transporters, have the flexibility in that the target ship can be raided in an attempt to destroy some of its systems. If you board a ship to raid it, it will often be destroyed as a result of a damaged engine, so if the target ship is heavily armored, this can be the easiest way to get rid of it. The down side of these methods is that transporters require the facing shield of the target ship to be taken out, and boarding with only tractor beams requires the boarding ship to be very close to the target. Cost-effective implementations are few and far between.
Telepathic races can use captured ships in the middle of combat, so if an opponent has a low ground combat bonus but good defensive tech, you can use his own starbase to destroy ground defenses. This is effectively done with high-mobility ships which Chris calls "death tide" frigates. The more advanced method is either a combination of neutron blaster or death ray with tractor beam, or transporters. This is very flexible, and in very long games I often use tractor beam, death ray, and sub-space teleporter to capture ships with a single marine before they can move.
Cheap tactics
Stasis field coupled with a virtually unlimited weapon, preferably a good beam-computer combination or an ECCM antimatter torpedo is the most cost-effective, though tedious, way to destroy a ship in the late game. Essentially, once you are within 3 squares of a ship, you can freeze it, and it cannot attack you. Since it is possible to release a ship, shoot it, and freeze it again in the same turn, you have nearly unlimited shots on a ship which cannot retaliate. Since stasis fields take up at most 75 space, a "wolf pack" of inexpensive ships will do the job at least as well as a single heavily-weaponed ship. If the opponent also has stasis field, then the wolf pack (the phrase "gnat swarm" may be more appropriate) becomes invaluable, as the battle boils down to a question of quantity and maneuverability of ships. This can only be countered by good use of initiative and massive instant damage or by phasing cloak. Stasis fields are banned in many multiplayer games, because they destroy gameplay and make battles very long.
The combination of phasing cloak and time-warp facilitator allows you to attack any opponents lacking time-warp facilitator with impunity, as long as your ship initiative is adjusted correctly. On one of your turns, you can uncloak and fire, on the next turn you recloak, and the opponent is unable to act in the intervening time. This brings up the minimal Antarean fleet. Use the preceding link for details.
Extreme ships
I'm going to use a damage measure which I call effective damage. This does not indicate the actual amount of damage done in every situation, but instead the amount done in an ideal situation, i.e. every weapon hits, there are no shields or internal systems considerations, and no ship is hit for an overkill. Since a typical ship has equal armor and structure, the achilles targeting unit doubles effective beam damage. Other doubling action is done by structural analyzer and Hyper-X capacitors (for one turn only), and high-energy focus adds another 50% on top of that. One caveat is that the benefits of heavy mount and high-energy focus together are not multiplicative. A heavy mount beam with HEF only does twice the damage of a normal beam without HEF, not 225%.
Big beam ship: With enough hyper-advanced physics research, you can shrink mauler devices to 13 space. Then with appropriate hyper-advanced research in other areas to shrink the special systems, you can fit a doom star with structural analyzer, hyper-X capacitors, achilles targeting unit, high-energy focus, phasing cloak, time-warp facilitator, battle pods, and 109 mauler devices. This ship can deal 130,800 points of effective damage in a single turn of combat, and do the same in the next "turn", if there are any ships left. The phasing cloak and time-warp facilitator was added so the ship is less susceptible to conventional attack. However, it can still be killed by a very-low-initiative ship with phasing cloak or the reflection fields found at Antares, so it needs good armor. There are also plasma cannon and auto-fire disruptor cannon analogs which can do 309,600 and 231,840 damage respectively, but these end up somewhat less effective because of enemy shields and beam defense for both types, and range dissipation in the case of plasma cannons. I tend to prefer the Mauler ship for two reasons:
Note that all of the above numbers can be increased substantially by a mercenary skilled in ordnance, such as Loknar.
D-FENS: I give this name to any ship with damper field, energy absorber, heavy armor, reinforced hull, and automated repair unit. A doom star fitted as such can take effectively 48,000 points of damage, and will fully repair 9,600 effective damage, or 14,400 if your race is cybernetic - equivalent to 9 stellar converter hits. Stellar converters only do 300 points of (real) damage against this ship, and it can reply with 400 from the absorbed energy alone (which can be enhanced by most systems in the disruptor ship). I experimentally pitted a weaponless D-FENS destroyer with beam-enhancing systems against the Guardian, and the Guardian was killed in three combat turns by the enhanced output of the energy absorber. Despite its vaunted damage resistance, this ship will fall to a pitifully small EMG attack, and is also rather easily captured. If you send a weaponless ship with energy absorber against a space hydra and place combat on "auto" the absorbed energy will get traded back and forth until someone dies - usually the hydra dies when you have tech at the 3,500 RP level.
$: People who kill the Guardian and try to build their own cool ships often notice the high cost of death rays and particle beams. It turns out the most expensive ship possible requires only Battle Pods, Doom Star Construction, Megafluxers, Particle Beam, and a "fresh" computer tech. One may think that Death rays are more expensive for the space they take than particle beams, costing 2.5 production points per unit space instead of 2.33... but by a strange quirk of rounding, point defense Fwd Ext (or Back Ext) particle beams cost 21 and take up 8 space, yielding 2.625 points per unit space. Hence, if you have no hyper-advanced computer tech, a doom star with battle pods, a moleculartronic computer, 260 Pd Fx particle beams, and 2 Pd 360 particle beams will cost 12,810 production. However, this is not the largest production task possible. Since refitting a ship costs either a set minimum cost or twice the difference in cost of the designs, refitting an empty doom star to the aforementioned will cost 17,620 production. Purchasing the production for this task will cost 70,480 BC's. Oddly enough, if you lack the necessary funds by between 32,768 and 65,535 BC's, the computer will say you are short by a negative amount. However, you're still not allowed to buy the ship.