Some shoes are available in various widths, some better for support, some for cushioning. The kid with the flat feet might need supports, Superfeet a good brand, Sorbathane also good, better for cushioning. These replace insoles that come in shoe. Yiou need to go to a good running shoe store, cost a bit more, but will get a better fit and good recommendation on a shoe for you.
Most of the injuries I see are due to lack of flexibility, stretch out before and after, start slow and not too much mileage.
New Balance athletic shoes are made in USA, and are not bad, but I prefer ASICS myself, gel 2120's I think were last ones i got. They have Podiatrist discount deal for like 50% off, which is not bad.
Check this
http://www.apma.org/MainMenu/RecommendedProducts/SealofAcceptance/ProductsbyCategory.aspx#FOOTWEAR