That all depends on what you mean by serious. However, generally, and based on the word "serious," I would say after the start of puberty.

I would offer at the earliest age possible assuming that by serious you also mean age appropriate. Proper training never starts too early.

i would say 12under because it will be easier for him/her when they get older

I'm 9 and I do some weight training and a lot of running. Agility drills and the Nike Sparq training are also good.