With Cheap guitars they make a zillion Strat copies and a lot of them are very playable... but.. a kid will want distortion. Cheap Strat copies have terrible PU's. So just make sure what ever you buy has at least 1 humbucker. At least a cheapo Humbucker will distort.
Another thing to think about is re sale value, A $200 no-name guitar when you go to sell it will get you $50 back if your lucky. A brand name, even if it's a POS will fetch more, some don't depreciate much at all like Gibsons and PRS. Gibson LP's are often a little heavy for teens.
Musicians friend is always selling G&L's for half price on Stupid deal of the day. I own one myself and it is one of the best production guitars I've ever owned (I've owned a lot)
PS, Last time I tried an Ibanez it was typical Chinese junk. At least the lower end ones are now, same with Yamaha who used to make great cheap guitars.