Well first off, I don't want to come off as condescending, but whatever you payed for that computer I am sure you could've chosen something with custom parts that you yourself can assemble for the same price with MUCH better parts... a 3450 is a rather weak card... but that's okay, it's still game worthy.. but look maybe to a cheap upgrade to an 9800GT or an HD4850 down the line (or whatever medium-high end budget card is available)..
and another thing, if you're going to get into PC gaming, at least with first-person shooters, I would definitely get used to a mouse and keyboard with the WASD layout, because you will get destroyed online with a controller... use the controller for other games, maybe racing or someting
anywhoo... with that in mind, I wouldn't recommend any graphic-intense stuff.. Firstly, get Steam (
Welcome to Steam), maybe start off by getting Orange Box.. you get all the Half-Life 2 episodes as well as Team Fortress 2 and Portal.. the great thing about Valve games is that they are very scalable.. I'm sure you computer will come close to maxing it out comfortably..
Get CoD4 or World at War, choose your pick, they're the same game practically with different themes, I prefer cod4 though..
Get Fallout 3, as its not too demanding either, it's mainly an RPG, but it has a decent first-person shooter element.
I'd highly suggest getting into some RTS, mainly Company of Heroes or maybe World in Conflict, or look for Starcraft II which should come out soon
And just avoid Crysis.. while it's a great game, your computer will be eaten alive
oh and do not be tempted by MMOs like World of Warcraft, there are enough ways as it is to have your life sucked into a vortex