From: François Blais
The regular, most common bass size is the 3/4.
The most important difference is the scale lenght.
For a 3/4, it's about 41.5 inches.
For a 1/2, around 38 inches, etc.
Unless your son is very young, or very small, I'd suggest a 3/4.
I don't know what your budget is, but you'll probably buy a plywood.
A decent quality carved instrument starts at about $3000 I think.
Other people can correct me if I'm wrong.
He may need a pickup if he plans to plug his instrument.
A good setup with good strings, a decent bag, adjustable bridge and accurate fingerboard shaping is also to be considered, IMHO.
Hope this helps!
François