Ta-dah! The Wild ARMs expert is here, to answer your questions!
I own all three of the games, and soon plan to own Alter Code F, the new one coming out eventually.
Wild ARMs 1 is the best by far. The overworld map graphics are good, but almost SNES level. The graphics in fights were probably good for the time, but quite dated by today's standards. The combat system is pretty average, though each character has unique abilities and there is the addition of the "Force Gage," which fills up when you perform an action/take damage, and allows you to perform special moves.
The storyline is awesome as well, and as stated, there are only three characters in the whole game, so you don't have to worry about a character getting behind in levels or whatnot.
Wild ARMs 2 is probably my least favorite of the series. Not because it's a bad game, just because it's not as good as the first. The storyline in 2 never really picks up like it did in the first. That, and I didn't care for the characters quite as much. However, 2 was indeed good, except for the fact that it introduced the "Search" system into the game. This is a controversial feature (that I personally don't like). Basically, none of the towns or dungeons are on the world map. You must press square and search for them to find them...of course, it's not totally blind searching, you will find out where to search for the towns/dungeons by talking to characters, but it's still irritating.
The 3rd one is my second favorite. It has a great storyline, great graphics, awesome characters, and it breaks a lot of the tradition of RPGs. For one thing, there is no equipment, and no magic learning system like in 1 and 2. It's hard to fully explain here, but play it and you'll see.
Any further info you want, ask me specific questions.