The first time I had my ears pierced, I was 12, and it was at a very reputable jewelry store. The second and third (in one ear) times were just in a Claire's-type place, I think. I've never had any problems, but be sure to follow all of the instructions about follow up care.
I just used the little gold studs, so I don't know about using stones. However, I've seen little baby girls with stones in their ears, so I'm guessing there are options.