Edit: I did not realize this was request-for-suggestion on an existing game. Some of the below may be completely irrelevant or unattainable in-place.
Note that the game is focusing on grand strategic level (no tactics, no moving ships around, etc) so the combat need be only as complex as to affect the strategic layer (what ships to build, what composition of fleet to send vs a certain alien race, how many to send, which upgrades to install). The combat is presented only in an observer mode (optional), so the player can see and learn how it all works together, not to issue tactical orders.
"You have various hulls, and you need to choose their design proficiencies, and group those into fleets." Given those design requirements, my first-blanch reaction is...
You have several size classes of ship. Let's arbitrarily call them Class-1 (one- to five-man fighters, strike craft), C2 (fifty-man small vessels), C3 (five-hundred-man frigates/cruisers/support craft), C4 (I think you see where this is going), where each class is approximately twice the length (four times the cross-sectional surface area, eight times the volume) of the previous.
Every ship has the same "nominal volume" for design purposes; that is, no matter what the size class, appropriate systems for that size takes up the same percentage of volume. Every ship needs thrust and fuel, so we'll set aside a static percentage of those that are just inherently part of every design. And then you can provide sliders for all the features your tech level provides, which must all add up to less than 100%.
There can be a feature "Streamlining", which eats up volume but increases maneuverability and reduces the ship's cross-sectional size, making it harder to hit with direct impacts (beam/kinetic weapons, penetrating missiles).
There can be a feature "Shielding", which eats up volume, but adds a % deflection against damage from EM weapons (energy beams, plasma, radiation).
There can be a feature "Armour plating", which eats up volume and reduces maneuverability, but adds a % deflection against damage from non-EM weapons (kinetic, missiles, torpedoes).
There can be a feature "Point Defense Weapons", which can target fast-moving objects at close range. For every 5% you allocate here, the vessel takes its size-class in shots at valid targets in range (missiles, torpedoes, and ships two or more size classes smaller).
There can be a feature "Main Armament", which targets vessels of the nearly-same class and fixed installations such as stations or planetary structures. For every 5% you allocate here, the vessel takes its size-class in shots at valid targets in range (ships no more than one size class smaller, ships of equal or larger size, fixed installations).
When you select point defense and main armament, you also select a weapon type in particular to mount. Different weapons have different properties. Beam weapons are deflectable by shields, kinetic weapons can be stopped by armour, flak and burst weapons hit multiple ships in the same Group, hull-penetrating missiles are less likely to hit more maneuverable ships but do more damage to anything they do hit, et cetera. You can mount multiple point defenses and main armaments to have multiple loads, but all weapons of one Group and one Type (point vs. main) use the same targetting choice each combat round.
Any space unused by features is unspent, reducing the cost of the ship from its base value.
All systems have a small extra % of effectiveness for each aggregate Tech Level of difference between the two fleets. Every system also increases in effectiveness for each level of Specialization research you commit to globally (each "Specialization" research being a penalty to one system in exchange for a boon to another), or you can add or cancel out Specialization levels for a specific ship design by paying extra on a per-unit basis (in the long run, the global is cheaper, but since the global affects all your fleets everywhere, sometimes you need to respecialize to deal with a rising threat). Larger ship classes systems are more effective than equal %volume of smaller ship classes' systems, but not quite by the full factor-of-two; you need to pump Specialization in to push it to or above a 2.0 multiplier relative to the next size class down.
And lastly... when you design a fleet, you give up to two really high-level order to each Group of homogenous hulls. "Attack (a size class | "deep-strike")" or "Screen (a Group)" or "Retreat" or whatnot. In battle, a ship prioritizes fulfilling its order. Deep-striking units can attack screened groups directly, but will be attacked by the screeners directly. If an order cannot be perfectly fulfilled, the Group falls back on its second order; if that cannot be fulfilled, it starts widening the orders it's given, choosing other size classes to attack, screening a different group, or retreating if all else fails.
With that together, you have a way for race-wide affinities to emerge (global Specializations), a way to customize how you deal with specific enemy ship designs (hull Specializations), a way to give fleets basic doctrines for using your design in battle (Orders), and a need to design fleets to either deal with a broad spectrum of foes or else specialize against a particular foe (e.g. your opponent's figher-swarm tactic is defeated by having large numbers of flak-based point defense on cruiser groups, which are set to screen your anti-capital-ship beam-mounting destroyers).
There can be a feature "Armour plating", which eats up volume and reduces maneuverability, but adds a % deflection against damage from non-EM weapons.