Pokemon is a turn-based RPG where you can basically add any random encounters into your team, and as such, very customizable, unlike most JRPGs. There is almost no limit to the amount of teams you could possibly have.
http://meta289.deviantart.com/#/d4j1eby The Pokemon Cycle. Don't deny its existence.
It's a turn-based RPG series. Best comparisons among games made by Nintendo would be Earthbound or Paper Mario. But the main characters don't fight; the random monsters you encounter can be captured and added to your team, and they do the fighting for you.
The versions usually come in pairs (Black/White, Heart Gold/Soul Silver, X/Y), and each game in the pair is nearly identical, so it doesn't matter which game from any given pair you get.
Recommended game? Depends. Black/White 1 for the story. Black/White 2 for the variety of gameplay options. Heart Gold/Soul Silver for the nostalgia you're unlikely to have. Platinum (which is essentially an upgrade of Diamond/Pearl, and I'd recommend it over either of them) for all-around.
X and Y aren't out yet, and we know little about them at this point, so no comment.
Creator of Jay's Journey (see quote!) "It's not ten years old! Therefore, it sucks!" - Nostalgia whores everywhere