I would say start with Freedom Unite for the psp. It's fairly polished compared to the older games, and has a tremendous amount of content. I don't remember, but I think I'm around two or three-hundred hours into the game, and I'm still not done doing what I intended to. There are people who play the game for 1000 hours or more.
With FU, you can play online with people using xlink kai or adhoc party, since you have a ps3, Nate. I haven't used these before, but I can probably help you hunt stuff. I'm fairly far into the game.
The learning curve is a bit steep, and the beginnings are a bit slow, but once you get probably 50-80 hours into the game, you'll start seeing what makes the series so good.
Oh, and you'll need this: http://monsterhunter.wikia.com/wiki/Monster_Hunter_Wiki
MH Tri is the newest game available in the west. I really, really love that game, but unfortunately I dont own a wii. It's much more polished and prettier than FU, but fairly limited in content. There are a bunch of other new games, too, but Capcom won't release them here for some reason.
Just let us know what you decide to do, and we'll brief you on the more important game mechanics, since the games themselves tend to do a bad job of explaining them.