If I was going to suggest which one to play first, I'd tell most people to start with Final Fantasy IV (or Final Fantasy II US) on the Super Nintendo, and follow that up with Final Fantasy VI (or Final Fantasy III US) also on the SNES. Those are the two best entries in the series, and both of them involve a minimum of level grinding and/or item hunting in order to progress through the game. In addition, FF VI is considered by myself and many other gamers who grew up in the 16-bit generation to be the best in the series.
Playing the first one now on the NES is probably an exercise in frustration for most gamers, as it lacks so many of the conventions that have become standard over time as RPGs evolved. You have to know how to time your attacks so as not to waste them, you have spell slots instead of MP, and level grinding is practically mandatory, especially in the endgame before you start taking on the huge boss characters. The remakes that can be found on the Game Boy Advance and Playstation 1 alleviate some of these problems, which makes them a little easier than the NES version. It's worth playing for the storyline though, which is fairly convoluted but kinda works itself out in the end.
After that, go to it in any order you like; they're all self-contained with the exceptions of the FFIV "sequel" story on the Wii, and Final Fantasy X-2 on the PS2 (well, and FF XI, but that's an MMORPG and should be avoided for that reason alone). And while it isn't a true Final Fantasy title, "The Final Fantasy Legend 2" on the original Game Boy is the best RPG on that platform, and really needs to be experienced by any RPG fan.
*huggles*
Areala