Here are some of my thoughts:

I think it would be wonderful if there were even more aspects to choosing Good/Neutral/Evil. Something like a Cloaking Device (which could end up doing any number of in-game effects from flat out bonuses to attack/defense or giving the cloaked ships a 'free' turn to fire on other ships... whatever) should be an "evil" only tech. Where something more passive like electronic warfare would be a "good" only tech.
Deathrays and Blackhole Creator weapons should be the farthest a team can develope without picking an alignment. But there should be a lot more juicy techs, ship components, planet upgrades, starbase upgrades and more for picking an alignment.

As for more weapon types? Currently we have a pseudo- Rock/Paper/Scissor set up. Not perfectly, but over all I don't think a fourth weapon type is all that necessary. If there were to be a fourth type, my suggestion would be drone fighters. I'm not sure what the defense for them would be.
But before a fourth weapon type was presented, I believe the current set up of beam/missle/m. drivers should be re-defined. First weapons should be given ranges. Missles should be long range. Mass drivers short range. Beam weapons in the middle. Second, weapons should use energy. When you put a engine on a ship, the weapons you put on it drain some of that engine to work (and maybe even armor could drain engines a bit too). Thus there would be a trade off between firepower and pure speed. Third, there should be other 'passive' parts for a ship other than sensors, life support, and trade/colony/troop pods. There should be Flux Capacitators that increase the amount of energy an engine gives to weapon systems (thus allowing more power to speed); beam focusers that increase the range of beam weapons; repair drones that can give a ship some ability to repair in space; the list could go on really. But stuff like this could really give the players truly unique ships.

Anyway, my 2 cents.

Why would Mass Drivers be short range?
In space, once an object is moving it keeps on moving with the same velocity until something acts on it.
A bullet shot from a ship would not have any range limitations in reality, so why put a false limitation in the game?

Beams are most likely to have an effective range since they tend to spread and lose focus with distance.

Why would Mass Drivers be short range? In space, once an object is moving it keeps on moving with the same velocity until something acts on it. A bullet shot from a ship would not have any range limitations in reality, so why put a false limitation in the game?

This would factor in that mass drivers fire in a straight line and by the time the round gets to longer ranges most target would have moved out of the way. Beam weapons are limited by the ability to produce energy and keep a focused beam. Missiles are guided, self propelled weapons that should have longer ranges and be harder to avoid by that logic.

As healdhj mentioned, mass drivers are basically machine guns on space ships. True they can technically 'fly forever' assuming they aren't effected by any gravitational forces at all. But they only fly in a straight line and only as fast as you can propel them with gunpowder or some other sci-fi tech like magnetics or something. Yet still, compared to beam weapons which is light speed. And missles which are basically little ships with their own engines (maybe even with enough techs could have cheap star ship engines and thus go pretty fast) the mass driver is the slowest and requires you to be almost on top of your target for the bullets you are spraying to have any accuracy what so ever.

With more ship components/techs there could a lot more customization with ships and their weapons/engines/defenses/modules. So you see a fleet of mass-driver ships and you assume some close up swarm fighters. To counter you build small but superior group of long range but expensive missle ships... or slightly longer range beam weapons. But uh-oh! That player added on some expensive Rail-Gun Magnetic Geostablizers on their mass-driver turrets, and now they have the range of beam weapons and out gun you... but you're an evil race and have cloaking devices so you can get the jump on his fleet as they zero in on your warp engine signatures...

Just cool extras that aren't just weapons would be great. Something to increase the strategy and customization past the current: "Ok, the Thalan have beam weapons and conventional armor.... so I'll just build a huge fleet of missle weapon ships with shields."

That kind of stuff is easy to mod in.

As for more weapon types? Currently we have a pseudo- Rock/Paper/Scissor set up. Not perfectly, but over all I don't think a fourth weapon type is all that necessary. If there were to be a fourth type, my suggestion would be drone fighters. I'm not sure what the defense for them would be. But before a fourth weapon type was presented, I believe the current set up of beam/missle/m. drivers should be re-defined. First weapons should be given ranges. Missles should be long range. Mass drivers short range. Beam weapons in the middle. Second, weapons should use energy. When you put a engine on a ship, the weapons you put on it drain some of that engine to work (and maybe even armor could drain engines a bit too). Thus there would be a trade off between firepower and pure speed. Third, there should be other 'passive' parts for a ship other than sensors, life support, and trade/colony/troop pods. There should be Flux Capacitators that increase the amount of energy an engine gives to weapon systems (thus allowing more power to speed); beam focusers that increase the range of beam weapons; repair drones that can give a ship some ability to repair in space; the list could go on really. But stuff like this could really give the players truly unique ships.

If you don't play EVE-Online I'll be amazed.

I'm not sure I want this kind of depth to GC2 ships, without tactical combat I don't see it being all that entertaining. This stuff works in well in games that give you fine control over your units where you can appreciate what is going on, in GC2 it could be a bit too much micromanagement trying to balance your fleet to use things correctly, geting the right ships built at the right time and assembling balanced fleets could be time consuming and just plain awkward.

In a game like Homeworld 2 it would be very cool.