I'd recommend all the GBA ports, and definitely FFIII for the DS. Of course, that's going to be over $100, but I'd definitely recommend them all. FFIV has a great cast of characters and storyline, with a good bonus dungeon and character selection near the end of the game. FFV has a ton of upgrades with four new jobs and a very challenging bonus dungeon. FFVI is a wonderful game, and although downgraded, has quite a few extras of its own. FFIII is a classic game, reborn in 3D with a rebalanced battle and job system. However, it also retains its old-school difficulty, which might be a turn off in deciding to play it. It's basically up to you which ones you want to get, although, I didn't purchase them all at once.

If you can wait until February, FFVI Advance comes out (February 4th, if I recall), and its definitely worth the wait. FFIV and V Advance are also already released, of course.
Also of note are Final Fantasy I and II: Dawn of Souls. With upgraded Wonderswan graphics and significantly decreased frustration to cater to the new generation, you can enjoy the first two Final Fantasies portable without having to tear your hair out in frustration due to ancient annoyances.
Final Fantasy Tactics Advance is a wonderful portable FF game set in the world of Ivalice, though a bit different this time. FFTA can get pretty addicting, as there are a plethora of different things to do in it, beyond the main storyline. You probably wouldn't want to do all of these things unless you were a completionist, however.
So, bottom line:
1.) FFVI Advance
2.) FFV Advance
3.) FFIII DS
4.) FFIV Advance
5.) FFI & II: Dawn of Souls
6.) FFT Advance