Suggested reading for different takes on space combat:
"The Lost Fleet" series by Jack Campbell pits huge fleets against each other with no fighters/bombers. It describes the use of missiles, beam weapons, and kinetic rounds against fleets and planetary targets. Also good reading.
The "Star Carrier" series by Ian Douglas uses combat at near c velocities as described early in the thread. I personally don't like this form of combat as a guide for a game, but it is well described and the books are a fun "B novel" read.
Another reference is something I've mentioned before: the game Horizon, which is available on Steam and which I've been playing with each new Alpha release as a reference. It is a 4x space strategy game with some similarities to GC. (Warning: the AI is too easy to beat so start on at least the Hard difficulty level.) Although ship design in the game is rudimentary compared to GC, what you put on ships matters a lot. Different types of beam weapons do different types of damage. Same with missiles and bombs. Fighters are important and are effective against any class of ship (they also make fantastic missile defenses). Defensive systems are also critical. Use ship mass for Cloaking so a fleet can sneak up on an unsuspecting world, or for Stealth which makes targeting your ships harder, or use your available mass to pile on weapons. Armor can be upgraded so that it can repair itself or you can use shields. Etc. It has tactical combat and a retreat option. Even planets can have weapons.
For GC 3, I REALLY want my ship designs to matter in combat (REALLY, REALLY). Missiles are long-range weapons (maybe even give them a range of 1 hex later in the game). They are also good for anti-missile and anti-fighter/bomber defense. Beam weapons are for "knife fight" range, really close combat. Large beam weapons like those in Babylon 5 would be used for anti-ship and targeted stationary attack, batteries of smaller beam weapons for anti-missile and anti-fighter defense. Kinetic weapons are fantastic for planetary bombardment or against fixed targets. Much less so against mobile targets unless you're close or can "pepper" space like a shotgun. So, large rail guns for massive damage, smaller clustered kinetic launchers for anti-missile and anti-fighter defense. AND, all of this could be done without including weapon arcs, which the developers have said they don't want to do. These weapons could also be placed on planets.
One last offensive combat comment: fighters/bombers should stay relevant throughout the game. In GC 2 later game, I would have nothing but fleets of massive hull ships. I had no need for smaller ships. I would like to have a reason in GC 3 to have fleets of different classes of ships. Look at a carrier battle group: a carrier, support cruisers, frigates, destroyers, and some submarines. Also refuelers and replenishment ships. Each ship has a role (air defense, anti-submarine, anti-ship), but each ship also has a compliment of weapons to deal with different threats. Fighters/bombers can carry weapons that can sink smaller ships and damage larger ones.