I'd go to the junkyard and get one used tire that will hold air and put it on the wheel that keeps going flat. Leave the wheels with the dry rotted tires on it while you work on it as rollers. Use the money you were going to spend on wheels/tires toward other things for now. When it gets near the time you'll be registering the car, have your (then older) son search for used wheels with tires. By that time, there will be a lot more choices available for used 17" wheels and he will have a stronger opinion on what he'd like.
The accepted usable life of a tire is only 6-7 years reguardless of mileage because the rubber dries out. so buying used tires now and putting them on the car doesn't really make much sense because they will be unsafe by the time your son gets his license in 5 years. Here is just one of many reports that have been done recently on the lifespan of automobile tires.
http://today.msnbc.msn.com/id/24390155/