Trying to put myself in your situation with a teenage son. Anything from a bike shop is going to cost you more than from a big box store, but you have some backup if something goes wrong with it. If you are mechanically inclined, then something from a big box store might work well for him, because you are likely to have to make adjustments to things like brakes and derailleur. How about taking him into a big box store and letting him choose a bike? Those would be fine if he's only going to use it to ride to his pals' homes. If he's going to be pounding it on some rough tracks then you'd want something a little more robust, and that would mean something from a bike shop. That doesn't mean a bike shop bike will be good for pounding on a track because their low end bikes are probably no better than the bikes from the big store. So you'd have to go to a higher price if it's going to get a bit of rough treatment.
Perhaps he can save his pennies and eventually upgrade to something with a brand name. Teach him to service his own bike; there are loads of of teaching videos on the internet. Oh, and teach him that bikes are one of the most stolen items, with little chance of recovery. Chains and locks might stop a walk-up, ride-away thief, but they won't stop those who choose stealing bikes as a profession.