A young surfers surfboard
Hi Lawrence, welcome to Surfing Waves.
Normally my advice is to get as big a board as possible, but this is not such good advice for a 4'8'' 10 year old!
I would think that a minimal board around 7' would probably be ok, perhaps larger if your would be able to handle it (it really is hard to say without knowing your son).
You want the biggest board possible without being too much of a handful. Pop-outs are a good starting choice - very bouyant and easy to catch waves, and have been designed with beginners in mind.
Price depends on whether you want new or second hand. If your son is an athletic snowboarder and skater then he should progress well in his surfing, and may be looking for a replacement for his beginners board in a short time.