WC gave a very good synopsis, but I'll chime in my two cents.

Don't feel you have to play though every game before you get to the next one. Opinion on each game is quite divisive, they aren't all for everybody. If I had started and played in order I never would have gotten past FF2. If you start to lose interest in a title move on to the next one, it will still be there waiting when you want to come back to it.


My recommendations:
FF3 - DS
I know of exceedingly few people who didn't play the original first that don't prefer this version.

FF4 - DS
Opinion on this somewhat split. For me they improved upon the original in just about every possible way. It is my favorite game on the DS.

FF5 - I highly recommend this, but I don't have much to say on which version.

FF6 - Ditto

FF7 - I am going to recommend the PC version. (I don't know if it works on Win7. You need to get a fan made patch to run it on XP) They changed the dialoge somewhat, but the big sell is that they doubled the resolution from the PS1 version.