We have a spesh rockhopper for my youngest. He had a 13.5" and now has a 15" (old womens fame I think). Built up not spending too much. Great comfy frames, and not too expensive used. We also have a 14" scandal for my oldest aged 12. Light, but not so good for kids (especially girls) due to the long top tube. I prefer the rockhopper for kids.
This is my youngest son with his new bike. He is 10 and about 145cm. Bike weight 24.7lbs (as in the picture incl heavy seat/pedals etc).
Spend as much on air forks and light wheels as you can. This bike cost about £350 (still had the brakes and shifters).