As others have said, the smoothness of surfaces and truing of axles and wheels are your #1 concern. Of course, you want the maximum weight you can have, too - and I mean really the maximum, use a 1/10th gram scale to be sure. Aerodynamics are secondary, so whatever the kid thinks looks cool is cool. I'd polish the bearing surfaces to a high mirror shine and use the best lubricant you possibly can. Liquid graphite may be all you're allowed. Maybe you could chuck the axles in a drill and spin the ends against a piece of 0000 steel wool. You don't want to remove too much material, however, because you'll make the wheels loose, so go slow. Polish the sides of the car on which the wheels bear to the same shine. A hard, smooth coating of something like acrylic nail polish on these surfaces might be good, as I'd be afraid that regular paint, varnish, or even bare wood could be a little more tacky and cause the wheels to drag against it. Polish the insides portion of the wheels where they meet the car using a peice of old denim for "sandpaper." It's probably best to not mess with the insides of the wheels, where the axles go, because that surface is probably already quite smooth, being cast. Still you could buy a few sets of wheels and pick the most perfect set using a micrometer, if one is available to you.
Not sure how to make sure the axles are perfect, but maybe somebody can provide some insight. I'd want there to be at most .010" deviation, but I'm not sure how difficult that kind of accuracy might be. Perhaps you could construct some kind of jig? Don't use a hammer to push the axles in, rather use a drill press to push them in smoothly, one by one, if you have one.
This sounds like overkill, but I grew up and was in boy scouts with a bunch of rich kids, and let me tell you, competition was cutthroat. At least two of the kids had actually put their cars in a wind tunnel at their dad's work to fine tune aerodynamics.