I found MH3U to be a good introduction to the series... or at least that's how I felt it being my first MH game.
MH4U adds a few things and I felt was a little more challenging, and unlike 3U you can actually play online multiplayer.
MHGen is the latest in the series and more likely than not has the most active online community. It does throw a lot of stuff at you at once which might not be so great for a beginner. However the "DMC-type moves" mentioned above do make the game easier, IMO. (It's also something I hope the tone down a lot or remove entirely in the next generation of games)
If you're not planning on doing multiplayer I feel MH3U has the best singleplayer. The entirety of low-rank is essentially a giant tutorial where you don't have to really worry about other monsters showing up to ruin your fight (unless you're fighting Qurupeco, which is the 'other monsters showing up to ruin your fight tutorial' monster.)
If you do want to play multiplayer... well it's a toss-up between 4U and Gen. I would say go with Gen simply because it's more active and
may be more indicative of what to expect from future games in terms of weapons, movesets, palicos, etc. The weapon upgrade system also gives you a better sense of progression than in the other games.
By the way, if you do pick up a Monster Hunter game, be prepared for 50 hours of gameplay to be the equivalent of pushing start after booting up in other games. You'll be sinking hours and hours into it... or you'll hate it and never play it again. it's not for everyone.
E: Oh yes, almost forgot. You can probably post in the
Monster Hunter thread and find someone who'd be willing to play multiplayer with you if you don't feel comfortable playing with pugs.