Over all the years of Trek gaming, my favorite would have to be Elite Force. Ironically from my least favorite of the shows, but it had a great story, great characters and found a way to balance being a shooter with all that entails and still staying true to the shows.
Dang it, now I have to go an install it for some retro gaming goodness!
Elite Forces! Very nice choice.
First Person Shooter: I am with you on that choice. Elite Forces is definitely at the top of the list. I loved the Borg in that game.
Space Simulator: Starfleet Command, Starfleet Command II, and Starfleet Command III.