I actually discovered Starsector on Fileplanet (remember that old site?) back in 2012 or so. I remember Alex had just added the first solar system so there wasn't really a galaxy yet to explore or interact with. It was basically just a combat sim at that point which is what endeared me to the game because even in that very early state, the combat was amazing.
For some reason, combat seems to be something that hardly any space games get right, even those that are fully 3D. I enjoyed Space Rangers 2 for example and the world was extremely well designed and dynamic but the crummy combat really crippled the experience because 90% of your success was based on stats rather than strategy or skill and later in the game you could just stack defenses to become virtually invincible. I've tried to get into Eve: Online half a dozen times or so over the years but the lame hands-off combat ends up putting me to sleep and so I quit.
Starsector on the other hand basically took the Mount and Blade approach to game design and I love it for that. They focused first and foremost on building a fantastic combat system to serve as the foundation and then built a world around it. And as much as I love having an immersive, dynamic and believable world in games, the combat system (assuming it's that type of game to begin with) really needs to be solid for all of that other stuff to be enjoyable for me. Other people are the complete opposite which is fine, but for me, the combat system and ability to build and customize your own ships/fleet is what sold me on Starsector. Exploration, factions, reputation, colonies and the like are just gravy.
As for my current fleet, for the longest time I've always liked to command a powerful capital ship myself like an Onslaught or Paragon. Although when I first started playing all those years ago the Hyperion was an unstoppable god-ship of doom and so I mainly used that. As for the rest of my fleet, I absolutely love Eagles spec'd primarily to disable enemy ships with kinetic and emp weapons. The AI piloting an Eagle is actually extremely good at staying alive and harassing the enemy which is why I typically have 5-7 of them serving as the backbone of my fleet. So basically I have the AI max out the enemy's flux and disable them while I finish them. Currently I'm using 4 HIL's on my Paragon which just burn holes right through most ships in a couple of seconds once their shields are out of the way. I also like to have a pair of Auroras to flank, harass and capitalize on overloads which the AI is remarkably competent at. I'm not a huge fan of fighters though so I usually only have 1 or 2 cruiser/destroyer sized carriers to harass and/or torpedo large targets.