Good news is you can pick up a Kinect holiday bundle for only $250. Pretty good deal since you're getting the Kinect which is an optional add-on plus some games for only about $50 more than you'd pay for the barebones system. Check the package to see if it comes with two controllers if you want to play with him or if he has friends come over.
Dunno how old your kid is but he might enjoy the Kinect. If he is very young, Kinect Sesame Street TV has good reviews, as does Dance Central 3. If he is a little more mature Need for Speed: Most Wanted and NBA 2K13 (not Kinect exclusive) are also well rated. Keep in mind these are Kinect games. If you opt for a bundle without Kinect, avoid them. Some games will have Kinect on the front of the box--it doesn't necessarily mean they can only be used with Kinect, but rather some will be Kinect compatible. Ask the guy in the polo shirt.
Keep an eye out for the game rating on the box. M is equivalent to R for movies. Halo 4 has an M rating but it's more of a soft M. Call of Duty and Assassin's Creed both have warranted M ratings.
The top rated kid-friendly regular Xbox games right now are NBA 2K13, FIFA Soccer 13, NHL 13, Batman: Arkham Asylum & Batman: Arkham City, Portal, Burnout Revenge, The Secret of Monkey Island, and all of the Guitar Hero/Rock Band games (require instruments). Some of those aren't new so they won't be full price. Something like Burnout Revenge or Monkey Island could be under $20.
Bad news is in about 12 months the Xbox 360 will be obsolete. Doesn't mean he can't keep using it but if every other kid is getting a new one you'll be hearing about that. The next Xbox will probably also be considerably more expensive--likely $400 or more. Haven't heard yet whether games will be backward compatible (play old games on new system). The 360 was but it usually made for a lousy experience.