Staring Ship, Ship trade-ups, and Final Ships
Having played four games (well, 3 YASD's and only one Victory), I typically start with an Explorer class ship. I generally find galaxy exploration to be the most interesting aspect of the game, so this ship is a good fit for me. I like the fact that it comes with a pre-installed Science Lab; and I especially like that it comes with a pre-installed Immunization Suite. (I explore almost all planets exhaustively, including their cave systems, having cave-dived down 42 levels in my deepest dive, so features that make it safer for my Away Team are a significant plus.) Explorers also come with a pretty good Crew size (hence bigger Away Teams) which also aids my style of play. Downsides include less cargo capacity than I would like, and a single weapon slot which (in my experience) usually comes with a very poor first weapon.
However, in the course of my 90-Sector Victory game, I traded up (purchased) 5 improved ships. The first four were just better Explorers. These trade-ups, individually, provided fairly modest improvements, but over the course of 4, I ended up with a pretty solid ship. I finished with 3 weapons: a Slot-1 weapon delivering 439 damage, with a 1-turn cool-down; a Slot-2 weapon delivering 1,839 damage, with a 3-turn cool-down; and a Slot-3 weapon delivering 5,247 damage, with an 11-turn cool-down. Through 90 sectors, these weapons met my needs. (I kept a fairly weak Slot-1 weapon, in order to have 1-turn cool-down on it.)
My final trade-up was to a Negotiator class ship. It provided at least modest improvements in all categories compared to my last Explorer, but especially Speed (Speed=290, officially qualifying as "Lightning"). This ship finished with a Shield of 12,474; Hull/Armor of 4,024; Sensor/radar with range 6, and targeting of 40; and a Warp-drive with a range of 5 sectors, and a 10 turn cool-down. (I sacrificed some armor, in order to get a speed increase of 15, on this item.)
I crafted a LOT of equipment, in order to get solid equipment in each category. However, I never made a Reactor that had 6 device slots (along with the 3 weapon slots), so I never un-locked the Cruiser class ship. Still, my final Negotiator ship was very satisfactory, overall.
I would be interested in hearing, not only what ships other players like to start with, but also how they typically progress (trade-up), and what kind of ship they typically finish with, in the course of a winning (or at least a fairly long) game.
Thanks!

Explore long and prosper!