My first time shooting a rimfire was a Ruger 10/22, its a fine choice for a first rifle. Probably not the easiest thing for a 12 year old to take apart.
The first rimfire rifle i owned was a .22 Henry, I like it.
A .22LR bolt action would also be good, Marlin and savage provide plenty of affordable options.
I used to have a very light savage .17 hmr, model 93r17. It weighed about 5lbs, shot well enough. Would be better in a .22, but as far as its size and weight it would have been well proportioned for a 12 year old. That being said, I no longer own it because I love my heavy barreled Marlin 917v .17hmr because it shoots better..