FASA was and probably still is the best system out there for a TOS era campaign. The TNG stuff produced was really crappy, though not entirely FASA's fault. They only had one season to go on (the first season of TNG) before they lost the license. It's also a shame they lost the tactical system. I liked their Battletech style ship combat way more than I liked Starfleet Battles' system. Less complicated, more fun.
Prime Directive (non-D20) probably runs a close second, though it is definitely an "alternate universe" type setting. I found the Prime Teams to be a very logical and intensely fun idea that should have existed in Starfleet anyway (and they kind of did eventually in Enterprise's 3rd season). I haven't played the d20 version, but I generally believe that d20 versions are watered down versions of better systems.
LUG's system (Icon) wasn't that horrible, but neither was it any good. A solid C effort. They did excel in the source material, though - their books were some of the best written, most informative, and best produced. Though I didn't like their system as much as the previous two, I still miss their gorgeous sourcebooks.
Decipher is the definition of failure in RPGs, CCGs, etc. There is a reason you got those books for such a good deal. I saw the whole line for sale at Gen Con last year (new) for $6 a book. It's a horrible system and it's also an unsupported system at this point. They stopped producing the line in 2007.
I'm not so sure I'm in love with your idea of using a computer game for a tabletop combat scenario. I'm not that familiar with those games, admittedly, but can you set up the scenarios any way you want to? Can you have more than one person playing the scenarios at a time? It seems like you would have one person having fun with the game while the rest of your group sat around on their thumbs.
Crap, now I'm all nostalgic for some FASA Trek...