At her age, the big thing is to have her try on running shoes and choose the pair that she says is most comfortable. Make sure they are actual running shoes though; some stores will offer cross trainers or trail shoes or walking shoes and say they're fine but I'd recommend real running shoes. Doesn't need to be anything real high-tech since she probably won't exactly be racking up the mileage. As she gets older and runs more she'll want shoes that coordinate with her footstrike (support, guidance, motion control, etc.) but for now just something middle of the line is good. Don't order them online though, make sure she can try them on--if a kids tries on a shoe and it feels comfortable walking around then they're less likely to get hurt in it and it's probably a good fit for their type of foot. Go to a Dicks Sporting Goods and have her try on a few different models of Asics. I used to coach at a small high school (7-12 grades) and a lot of the younger kids wore the Nike Pegasus.