Most of my fleet is a toolbox of flagships. One Onslaught or Paragon, one Dominator, one Eagle, two Medusa, one or two Hyperion, one Lasher, one Scarab (no-brainer starter ship) and two to four Tempests. Every non-pursuit battle gets solo'ed by one ship. Battleship for simulator-sized extended battles, cruisers for detachments, Medusa for smaller fleets, and Hyperion for anything up to a single detachment-sized fleet. For pursuit, Lasher with Safety Override is cheap and efficient at mowing down defenseless targets. If targets are fast and/or dangerous, Tempests led by Hyperion or Scarab get deployed. (If it is too dangerous, I auto-resolve.) The only time I deploy more than one ship by endgame is during some pursuit battles when a lone Lasher, Scarab, or Hyperion cannot wipe the enemy fleet by itself.
I solo fleets because it consumes the least resources and protects the AI from itself.
In addition to fighting ships, I may bring one to three Atlases for looting multiple encounters in completely hostile systems (e.g., Eos Exodus), and as many tugs as I have slow ships. If my slowest ship is my capital, then one tug to bring it up to burn 9. If my slowest is my three Atlas, then three tugs to raise burn to 8.
I try to avoid beginning my raids with more than fifteen ships because boarding everything will fill my remaining fleet slots quickly. When I want a new ship, I try to board instead of shop for it because boarding can be cheaper than shopping.
Fighters in 0.7.2 are too weak in the endgame and are not worth using. Because fighters are not worth using, carriers are also similarly useless. Ships without flight decks are better at fighting or more efficient at hauling cargo.
Officers are used primarily to keep my flagships at 100% CR so I can stay in battle and/or chain-battle even longer. Officers rarely fight in the ships they get assigned to. I take over their ships as needed. Like I wrote above, my fleet is a toolbox. Pick the one tool that is most efficient the job and fix it (read: destroy enemy fleets).