Either Monster Hunter 2 for the Playstation 2 or Monster Hunter Tri for the Wii. You can probably find a copy of Tri in the bargain bin at a Wal-Mart for like ten bucks. It's the most recent iteration available in North America and quite good, but I haven't played it as much as 2 (and 2's expansions).
Monster Hunter 2 might be a little harder to find since it would probably be used, but it doesn't really lack anything substantial enough to justify passing it over to find Tri. They're both fantastic. If you have a PSP, Monster Hunter Freedom Unite is what you want. (Or Monster Hunter Portable 3rd if you don't mind reading Japanese, it's basically a port of Tri for PSP. Also you'll probably have to pirate it.) Freedom Unite is the expansion of an expansion of a port for Monster Hunter 2.
These games are balls hard, so be prepared to do a little shameless guide-reading to get your feet on the ground. The best advice I can give (that another player who is much better at the games than I gave me) is this: You see those gigantic Anime swords they wield in all the trailers and on the covers and shiz? The impossible slabs of metal and the giant lances/cannons? Avoid those. Start out with the more basic weapons of Sword and Shield or Dual Swords. The big weapons have a use later on, but they're tricky and cumbersome when you're just starting out.
Basically let's say you have a Sword and Shield weapon that does 200 base damage (ignoring the bazillion other stats that affect things) and a Greatsword that does 400. Despite the higher damage for every single strike you'll get in with the huge sword the smaller, faster option can get about 2+ more attacks in. Eventually the Greatswords deal massive damage and it's a matter of preference.
AND ANOTHER THING
BE prepared to do a lot of grinding for specific weapons and armours. once you have a nice little arsenal put together you won't need to repeat some missions as much, but if you want to avoid being 1 hit KO'd it's a good idea to grind the hell out of Khezus, Giadromes, Nip Nips, Faaaahs, Spodaroos and Royligoils.
Oh yeah, this website is your bestest friend:
http://monsterhunter.wikia.com/wiki/Monster_Hunter_Wiki