Wing Commander III would be my first suggestion. The FMV cutscenes are awesome. Mark Hamil, Malcolm McDowel, John Rhys-Davies, Biff from Back to the Future, Ginger Lyn Allen trying to transition into actual acting and Tim Curry as a spacer tiger man. Top notch. It's also the only one I have played all the way through. I do have WCIV on a shelf waiting to be played.
WC1 is pretty good but would suggest the 3DO version Super Wing Commander if you can emulate it. It's the most enhanced version of the first game. The Sega CD version is solid, the SNES version is bare bones and I have never actually played the PC version so have no opinion.
And by awesome I mean totally sweet.