I've ran and played both the FASA Star Trek RPG, and the original Prime Directive. I like them both immensely. FASA gets the nod for being more accurate to the source material, but Prime Directive is a lot of fun a s well.
Prime Directive takes place in the same universe/timeline as Starfleet Battles. These games are based on a license from Franz Joseph and Paramount. It's basically TOS up to the first movie. Of course there is no mention of any Kirk, Spock, etc., but it does contain ships, aliens, weapons, etc. from the original series.
The FASA game is out of print, but can be found on Ebay and used game stores. Prime Directive is still in print. As far as Decipher's version I have the main rulebook, but haven't had the chance to play it. From reading the rules though, it does appear to be more rules oriented than the previous games.
As someone else mentioned I would suggest Federation Commander for ship battles simulation. I have played Starfleet Battles for many years, but have switched over to FC for it greatly improved simplicity. For a casual player I believe it would be the best choice.
Good Luck with your games!