Coldhearted Snake Key for Dead Rising - 12/8/2006
It was my first game but I didn't get it until a few days after the console arrived. I got a great deal on the 360 Pro, $320, but the games were all full retail so I shopped elsewhere. I was honestly surprised when I looked at this that I got the DLC for that game before downloading a ton of demos.
I believe my first paid item was Contra, but I got it through a promotion so it wasn't me who paid. I'm too lazy to go through 20+ pages (thank god I stopped downloading videos on the marketplace) to find the date.