I always divide my warships in two categories :
Escorts :
DD - Destroyer - small weak ship designed to be used as a system defense in huge numbers
CL - Light Cruiser - bigger version of DD, primarily used for Anti-Missile defense
CA - Heavy Cruiser - similar to CL but with minimal Anti-missile defenses and with more ASM launchers
Capital Ships :
Usually they are designed to have far more range ( as in fuel ) and with shields and ECM's.
BC - Battlecruiser - large version of CL
BB - Battleship - large version of CA
DR - Dreadnought - large version of BC
SDR - Superdreadnought - large version of BB
and sometimes
MN - Monitor - huge and costly as frakk but "selfsufficient"
Utility ships:
MSS - Military support ship - mixed collier/tanker with civilian engines and almost no weapons but decent amount of armour/AMM's.
EX - Exploration ship - exactly what it sounds like - civi engines, some basic weaponry, grav/geo sensors.
Adding to that
Civilian Fleet :
Standart colony ship
standart cargo ship with Troop transports ( i dont make dedicated military troopships )
Terraformers
Salvager with tractor beam and salvage module, spare crew quarters ( for picking lifepods ).
and again sometimes i roleplay and built huge "astro Stations" with biggest active sensors possible, troop modules ( on-board marines ), hangar decks for small fighter/corvette/FAC sized ships ( Customs Police ) and tow them to JP's/various places around systems to feel somewhat like playing game in Honorverse ( ACS 4 lyfe )
Oh and i dont bother myself with Carriers ... too much micromanaging ( good salvo and 1 fighter wings suddenly divides into 5 parts coz they had various engine hits, fuel tanks etc ).