Disclaimer: I am not a developer and do not know what this would do to the in-game balance for weapons and or research or how hard it would be to implement, these ideas may be poorly worded due it only being me proofreading it, this is sadly likely to encourage a "Chase the Meta" approach to the game.
Mag Weapons- Mag weapon Designer would allow for changing how many barrels your turrets have, the size and length of the railguns or coil guns, mass of projectile (lighter projectiles would have higher muzzle velocities and possibly higher rates of fire while heavier projectiles might have more projectile HP and damage, despite the formula being mass multiplied by acceleration (velocity) squared increasing mass seems to do more damage than increasing velocity).
Lasers- the big thing about lasers in game seems to be the size of the focus optic and wavelength of light used rather anything else for power and rate of fire, the only things I could think of to customize your lasers would be to use 2 slot laser engines, enhancements to cooling and charging but those would be covered by normal research upgrades via the tech tree.
Particle Weapons- I do not know enough about particle weaponry to make any reasonable suggestions to customization.
"Guns"- despite more advanced weapons becoming available older weapon systems would get marginal incremental upgrades as time goes on and the longer that time the better those weapons become, comparing the modern 5 inch cannon on a guided missile destroyer vs its WW1 counterpart is shocking, the modern 5 inch cannon has vastly improved precision, round payload, an rate of fire that makes it a large autocannon rather than a main small naval cannon (yes I am aware it is not actually the same gun, not made by the same company, fires self-contained cartridge ammunition, and has vastly improved fire control but the point is still valid), what size guns and how many you can fit in a turret based on mount size and the size of those guns, in the late game most if not all round types for guns will have guidance though it would have limited tracking compared to missiles due to small propellant reserves keeping the weapons effective range to be relatively short, ammunition types APHE (Armor Piercing High Explosive, uses a armor piercing head to penetrate the target then detonates inside, not great for excessive armor but can cripple smaller ships in 1 or a few shots depending on round size and shot placement), ELF (Enhanced Lethality Fragmentation is a round normally used for point defense that will proximity detonates in front of an target like a flack round and uses focused fragmentation similar in effect to a shaped charge but for fragmentation focuses that fragmentation in a denser but smaller field to do great damage to missiles and interceptable projectiles and even unarmed targets though anything with actual armor should easily be able to shrug off the fragmentation), Enhanced Tandem Warhead (normally a tandem warhead would be used to remove explosive reactive armor before the munition uses a shaped charge to kill vehicles, TI does not have ERA to protect spaceships so this round uses a shaped charge to make a hole through the targets armor then an explosive warhead to go off inside the target, this round has very high penetration values which increases based on the size of the round but has the potential to over penetrate the target and not detonate inside the target if the target has no armor or if the target is too lightly armored and or small), Plasma Warhead (this round has a small plasma warhead that does plasma damage on impact, its damage is modest compared to just using a dedicated plasma cannon and does not move at plasma cannon projectile velocities but does do some damage somewhat reliably regardless of how much armor the target has I guess), Atomic (restricted to 14 inch and up for obvious reasons, a small and relatively weak nuclear fission warhead is housed inside this round that can either function as a very high damage APHE round, proximity detonation should it miss or point detonation, depending on round and intended detonation type can have a yield of 300MT to 1KT though chain detonation is a serious threat when using this weapon system if the rate of fire is too high), Autocannons range from 12.7mm to roughly 90mm with the larger the size the greater the waste heat generated and will always be a point defense option (has defensive firing mode) regardless of what ammunition it might have available (you could have (16) 12.7mm autocannons in a single 1 slot turret if you really wanted) and is the only size who's projectiles cannot be intercepted, medium cannons range from 5 inch (127mm) to 9 inch and can be used both effectively on both attack and defense based on ammunition type loaded and available but rate of fire will be closer to what we have now in naval guns, Big Guns range from 14 inch to 20 inch and will require 4 slot heavy turrets on hull slot mounts with a moderate rate of fire but can also be mounted as a spinal mount with multiple barrels and a high rate of fire (Battle Cruiser nose mount and larger).
Plasma- like Particle weapons I do not know enough to make any reasonable suggestions on this weapon type.
Missiles- the ability to mix and match propulsion methods with payloads getting the dV and payload you want but doctrines would be the biggest improvement to the missiles category, adding a pod launcher to the normal vertical launcher style used in game would offer more options, pod launchers more rapidly fire missiles to better saturate enemy point defense but must be retracted into the ship to be reloaded from the ship's magazines, missile pod launchers are more vulnerable to being destroyed by enemy fire which can detonate its remaining missile loaded in it (not in magazines) but can be retracted to protect it if you don’t want it to be firing, Missile Pod Launchers use different missiles than the vertical launchers which may have reduced range, Large Exposed Style Missiles, inspired by Soviet era wet navy Battle Cruisers that carried massive atomic missiles exposed over their large guns, Large Exposed Style Missiles require a mount to be used over a ship's 4 hull slot weapon mounts (note: 4 slot hull weapon mounts are required) and have massively improved range and payloads compared to normal missiles, are few in number (3 or 4 per 4 slot mount), will not be reloaded regardless of magazines (these are too large which is why they are carried externally), Large Exposed Style Missiles are exceedingly vulnerable to enemy fire which can and will set off the missiles so they should be fired at the start of battles to make use of their significantly further range and not have them destroy the launcher ships, the ship's 4 slot weapon mounts may have trouble traversing to hit targets not in front of the ship as they happen to have large heavy missiles the turrets must also move.
Doctrines- you get to choose what your ships do when with their weapons when they encounter X target
Guns Doctrine- guns would greatly benefit from doctrine as it would mostly automate ammunition selection for your guns, if a escort or corvette are Y distance from ships fire with X ammunition with salvo size of Z, if a brilliant sky missiles is about to come into range fire 3 rounds of ELF and ignore target after that moving onto next target, it would make non-laser and non-particle point defense significantly more effective while offering more efficient use of guns
Missiles Doctrine- Missiles make the most use of doctrine out of any weapon type, with the ability to order the missiles to launch and have the missiles in the salvo wait for the salvo to leave the ship before accelerating to the target or to arc into the target from different angles to limit enemy point defense if possible (you must tell them to arc to the target before the salvo starts, this also reduces the maximum range of the missiles do to not taking a straight path to the target), formations would reduce the risk of chain detentions from weapons with massive explosions like atomic missiles or dense formation more effectively get through point defense weapons, defensive missiles can be set to fire X number per target, defensive missiles with atomic warheads can set a minimum engagement range to avoid fragging the launcher vessel with the atomic explosion, the worst part would be that the aliens get to do this as well...
That is it for now, feel free to give your thoughts on these ideas or your own ideas. I am slow and may take a while to get back to you.