I just got an xbox too (my brother).
So far we only have two games, both of which i recommend. First is of course Halo. The second is Full Spectrum Warrior which kicks @ss. I havent stopped playing it for 2 straight days, except when i had to study for finals. But you dont shoot, u tell ur two or three groups where to go, where to fire, to give cover fire, to fire a grenade, etc. Very awesome.
Im also going to get Splinter Cell: Pandora Tomorrow whenever i get money. And my friend had a small game called Fushion Frenzy which was pretty cool if you play with four people.