I prefer Xbox 360 but PS3 is by far the better bang for your buck. With PS3 you get a built-in blu-ray player and free online play, whereas with the Xbox if you want to watch HD movies you have to purchase a separate add-on. Also Xbox charges like $70 a year to play live.
That being said, online play on the Xbox is waaay better than it is on the PS3. More people and better servers...I'm sure this will be disputed :)
As far as the Wii goes, it can be fun with other people, but in my opinion gets old pretty quickly. The games are fun and I see why it's appealing, it's just not my personal favorite. I'll stick to my original NES :) Plus, both the PS3 and 360 now have motion sensing capability which basically nullifies the appeal of a Wii for me.
PS3 and 360 have better graphics than the Wii, and frankly they have better games too. However, my parents are about your age and have a Wii, but they've used it like 3 times in 3 years. It really comes down to what kind of games you want to play. If you like the older arcade or family style games, like my dad does, then the Wii is probably your best bet, but if you're interested in modern style gaming my vote still goes to the 360, even though I hate Microsoft.
Just go to Best Buy or WalMart and test them out for an hour or two
But whatever you do...DO NOT get an Xbox 360 Arcade version. They are cheap but will cost you more in the end because they only have 4GB of storage