I can play Chaos Rings on my 1st Gen iPod Touch running iOS 3.1.2, although there is a lot of frameskip to keep the game running at a decent clip.
As far as I know all of SE's iOS games except for Voice Fantasy are playable on the original iPod Touch with its max firmware (3.1.3). I have Chaos Rings, Hills and Rivers Remain, and Vanguard Storm. I haven't bothered with the Final Fantasies because I already have those for GBA and DS. According to iTunes, you can run Final Fantasy III on an iPod Touch with firmware as low as 3.0.
I've been considering getting a newer model of iPod Touch just as a handheld gaming console; newer iPods are on par with iPhone 4 (processing power, high pixel-density, etc.). The problem is that they are rather pricey and I just dropped a lot of dough on a 3DS, so I'll probably hold off for a bit until they come down or I can get a good deal.