I dont know where you will be hunting, but I am very shocked no one has brought up the 30/30! It has everything you need for a good all around rifle that he could use for the rest of his life for anything...deer elk or black bear. Its not going to have the accuracy at longer ranges, but anything within 150 yards or so will fall if he does his part. Plus there are hundreds of 30/30 rifles out there on used gun racks that can be had really cheap...just add bullets and a good scope and an elk tag!
If you want to go the bolt action route, I would say a 7mm-08 is the way to go. You can even get one in a Handy Rifle really cheap and they are very good shooters.