I just started it myself last week. It's rather confusing, though I'm level 14 already, which means I have a spiffy new ship that's not quite as terrible as the one I started with. (I probably should have gotten an Escort, so that I could end space battles more quickly, but I went with a Cruiser instead, because I couldn't resist having a ship that looked like the original Enterprise)
Your XP are "Skill Points", and can be directly used to increase your captain's abilities. There's also "Expertise", which is something similar to that, but for your crewmen. I haven't figured out how to learn new abilities for them. (Keeps telling me I need training manuals, with no indication of where to get such manuals)
What confused me the most is that the missions seemed to stop for a while when I hit level 10. I had to do some PvE-queue things before I could resume doing story-ish missions. And then I started fighting vampire ghosts in a spooky haunted basement.
I'm kinda enjoying the game, but I'm not really excited about it.
Anyway, I'm Lt. Commander Drakar (of the USS Righteous Indignation - well, Rgts Indignation. The full name was too long) @ zazelby.