I played 1-5 and only finished 1, which I started on, and 3, which is currently my favorite even though I know it shouldn't. If you want to play them all, start with 3 on the NES because it's easy but it's hard enough to warm you up for 1. If you want to just try one to see if you like the series, go for 4 or 6, which are supposedly the best. Skip 2 regardless because iT SUCKS LIKE A LOT DON'T EVEN GET ME STARTED. You don't really need to do any research on them, but if you don't really play JRPGs, it might be a challenging game. 1, 2, and 3 are definitely the hardest, and 5 is a giant grind fest. I didn't get too far in 4, so I can't say much about it, but it definitely has the best plot of the 5 I did.
Regardless of which game you pick, PREPARE FOR MASS-GRINDING. I think 3 is the best in terms of grinding, since if you properly change your classes, you only need to grind before the final dungeon iIrc.
Also I highly suggest trying out the spin-offs Bravely Default and Crystal Chronicles (the first one. never played the rest of the series). I've heard only good things about the former, and it has an excellent demo you should play if you have a 3DS. The latter has a lot of nostalgic value to me and is a pretty good "casual" action RPG. That's not to say it's an easy game, of course, it's just very simple and grind-free.