So lately I try for more "themed" runs - but I tend to fall back to the same Ships/Builds quite often - not necessarily for combat efficiency sake but for convenience:
a) First cruiser: Is ALWAYS going to be an Eradicator
Why? Burnspeed 9. I don't do "naked" exploration (e.g. single dram or two frigates and a freighter), so I value hitting 20 burn with navigation.
b) Freighter: - Atlas only
Why? Safe for the VERY early game there is no reason not to run it. I tend even to spend story points in the order of Flagship -> logistics -> rest of the fleet.
Simply because I keep this thing indefinitely. S-Mod exp. cargo holds + Insulated engines + Bulk Transport + Navigation -> 18 burn speed. If I need to hit 20? Attuned Drive Filed (mod I consider mandatory). Somehow I just can't find any reason not to look around for one - after the first few missions.
c) Cruisers: Mostly Eradicator (purchased from the pathers with AAF), SO-Aurora for myself (never for the fleet - (still) to expensive for what it does), Sometimes Champion (I really like the slot combination). Here I see more potential for me to experiment - here is where my variety happens.
d) Capitals: Executor all the way!
Why? Only decently fast capital (beside Odyssey player only), I have tried them all. I do like the conquest which is able to keep up, but suffers GREATLY from PL-missle spam an swarm tactics (Endgame Knights of Ludd and such) due to the *** shield. Combat wise I have also run Onslaught, Paragon and Legion to great success - but waiting 1,5 minutes with in-combat time compression until something happens is so hard. Also: when running mostly capitals you always get swarmed - so large shield arcs are somewhat mandatory.
Onslaught: it IS fast enough in players hands - but the AI doesn't burndrive enough for my taste. I would love a hullmod "thruster-reroute" to turn burn-drive into maneuvering jets. @Alex -> would that work with AI?
Paragon is just slow as heck and kind of boring (compared to full on Onslaught dakka) but I personally find it necessary (or convenient) for some of the tougher challenges (super-redacted, mod end-game content)
Frigates and Destroyers are fine I think though I avoid low-tech here due to horrendous flux stats and not enough tank to do the "who needs shields anyway" game of the Onslaught/Legion
So that's about it - change my mind or side with me

(side note: I have not been able to force myself to do an all ought missle spam run Gryphon/Pegasus - so no comment on those - one or two gryphons have not had great success in my fleets)