A Start for a 10 year old
I agree that a .40 sized glow trainer is the best way to go if you are both seriously interested. It will cost you about $400 between the $300 or so for the plane plus AMA and club memberships and such though.
If you think it might be a passing fancy, try some of the small electric park fliers. There are several good ones, and some odd ones that still fly well. The firebird line is really easy for someone with no experience and no help to get to fly, but they don't fly at all like many other RC planes. One of the guys at my local hobby shop took 3 Firebird Outlaws to a family picnic. He had an 8yr old flying it around by himself after about 5min of instructions. These small electrics don't handle wind very well at all, but on the plus side they are much safer (though nothing is totally "safe" of course). One of the best more conventional electric trainers is the Slow Stick. There is a lot of good info in the electrics forums for more specifics on electric power.