Yes, I'm trying to apply reason and economics to military procurement in the BT Universe. I am aware that this is a fool's errand.
First question, do C-Bill costs matter?
We assume that C-Bill costs mean -something-, or they wouldn't put prices on components. So military production in the BTech 'Verse cannot be purely limited to 'buy everything that every construction line can produce' - if this is the case, C-Bills don't matter, all that matters are production lines (and in the medium to long term, those 'excess' C Bills would go to building and expanding production lines, until there is no longer a production line constraint).
Now, C-Bill costs may not be the only factor. In the short term, there are only so many shipyards, and you cannot merely wish them into existence - each shipyard represents time and c-bills and trained people building shipyards and not doing other things while they are building them (however note that whatever the cost of the shipyard, it is in a way 'baked into' the actual ship costs - the cost of building/maintaining infrastructure to build the thing is a part of the cost of the thing)
Further, for Warships/Jumpships specifically, it may be the case that in the short term, all the C-Bills in Comstar wont buy you people able to design and build compact cores. In the medium to long term, once a thing is known to be doable, and a general idea of how to do it, being the second (or tenth) nation to figure it out is far, far cheaper than being the first - and that is not counting intelligence work, turncoats with technical data, etc.
Based on the above, some observations:
1.) Capital Ship costs do not scale linearly with combat power. All other things being equal, something like Leviathan is more than a match for the same C-Bill costs of lighter warships in a stand up fight.
2.) Capital Ship costs inflate VERY VERY RAPIDLY as a result of adding docking collars, with the increase in cost based on the underlying cost of the K-F Drive. Adding a docking collar to a Leviathan costs a lot more than adding a docking collar to a Fox.
3.) Capital Ship costs also inflate from K-F Batteries, though the impact is much more flat - the KF-Battery on a corvette may nearly double her cost, while the KF-Battery on a major combatant represents a much smaller percentage of her cost.
4.) Combat Dropship costs are incredibly high, relative to combat power, when compared to warships.
5.) Fighter Carriage may be a false economy. While fighters are quite inexpensive for their combat power by comparison to combat dropships or warships, their support cost (fuel, munitions, care and feeding) are relatively higher than a warship - design a large fleet carrier and then figure out how much space you are dedicating to fuel alone, issues with sufficient bay doors to handle that fighter swarm in a reasonable period of time. Some of this can be ameliorated by dispersing your fighter assets to dropships - but see points 2 and 4 above.
If we assume C-Bills matter, and that a given great power anticipates its mission will include combat with a peer opponent (so the SLN doesn't enter here - their entire design philosophy indicates that they have no peer opponents), and that the ability to defeat that peer opponent in combat is a pressing national interest, then:
1.) Build big. Build as big as your yards can handle. The big mean units will form the core of your fleet, and there is NOTHING more expensive than a second-best navy.
2.) Small units should be built only when they fill a role big units cannot. One role is sheer coverage - if 3 Corvettes cost as much as a BB, yet cannot stand up to a BB in combat - those same 3 Corvettes can be in 3 places at once, whereas the BB can be in only one... and even a 'mere' corvette will be able to stand off an invasion force supported by far more than its cost in combat dropships.
3.) LF Batteries will depend on the role of the vessel. The are a relatively small cost on a BB, and represent a hugely expanded capability. That same expanded capability may increase by 50% or more the cost of a Corvette - so you have to weigh the pros and cons of having 3 corvettes that can only single jump, vs 2 with a 100% greater range. Mileage may vary. Even so, assuming that our BB's have LF Batteries, we may have to accept the cost of putting them on the whole navy - or else we get a 'homogeneous fleet speed' problem, Succession Wars flavor.
Dropcollars are a problem. Warships generally rely on Droppers for work as colliers, for mission tailoring, and for dropping forces into combat. But Drop Collars do insane things to the cost of a warship, and that is before you pay for the PWS that one is carrying on those collars. So we maybe eschew warship carriage of PWS, and use Jump Ships to bring the PWS along with the warfleet... but then the fleet isn't using its KF-Batteries, and has a large, vulnerable Jumpship component that it relies on to deliver additional, C-Bill inefficient, combat power. (due to cost multipliers for dropships).
Maybe we eschew PWS and Combat Droppers generally, as well as eschewing docking collars on warships. Use the C-Bills saved from those docking collars and PWS to simply buy more warships. Fleet Supply/Collier work can be provided by Cargo 'Warships', which can keep up with the main force, and far better defend themselves when necessary than the same cost of Jumpers and Cargo Droppers. For offensive operations, a small number of purpose built 'assault warships', which either accept the (heavy) cost of docking collars and Military Transport Dropships, or which focus on using space-dropped mechs backed up by local aerospace superiority to secure a beachhead, and then large cargo support craft to carry down the ground forces, might be sufficient. In the alternate, as jumpships have the same strategic mobility as even an LF-Equipped Warship, we could use standard jumpships carrying military transport dropships to carry our planetary invasion force. Though now that we've gone down the Lithium-Fusion Rabbit Hole, I like the idea of being able to 'threaten' any world within two jumps at a (strategic) moments notice, rather than one - both offensively and defensively, squaring your threatened area seems to me to be worth the increased cost.
Summary: In light of cost constraints, and assuming that CBills are a meaningful constraint, propose that a clean sheet Battletech Verse navy for a power concerned with fighting peer opponents would consist of:
1.) Battleships, as large as the slipways can handle, with intent to enlarge those slipways. Desired thrust, armament, and cargo capacity is a separate discussion, dependent on the threat environment.
2.) Corvettes, for situations that do not demand Battleships. Classes between the two may also be considered as necessary to fill specific roles, as such roles are envisioned.
3.) Compact Core Fleet Colliers, with full KF Support, large cargo stowage, and sufficient cargo shuttles to move the supplies to the warships. In the alternate, it may be appropriate to move the cargo storage from the Colliers onto the battleships and corvettes - building such vessels larger to incorporate all the supplies necessary for expected deployments. Self Defense/Anti Fighter Armament.
4.) Compact Core Planetary Assault Ships: Mech Drop Bays for a beachhead, 'Dropshuttles' for bringing Mechs to the surface once beachheads are established, self defense armament. Possibly bombardment weaponry and organic fighter support, or those roles may be left to the fleet vessels.
