My kids, 7 and 5, have their own digital cameras. They are hand-me-downs from years past and they are probably worth $20-$40 on eBay now. Be aware that kids can be rougher on gear - not because they will be so on purpose but they will be in situations of rough and tumble play more so than we adults (or maybe not
). My 7 year old son has already dropped and rolled his camera down the side of a hill. It survived but it's also a $20 6MP Kodak. He freaked out more than I did. Lesson learned. Yes, they will touch the lens.
I say go cheap and if the hobby/activity sticks then get them an upgrade next year. My kids don't care about megapixel count, IQ, 100% crops, etc. They just want to snap photos and have fun.