Ya, sports are a great way for a younger kid to stay fit. That's what I did when I was that age, and still do.
But workout wise, using machines and free weights isn't what he needs. Just getting him to do stuff with his own body weight will probably benefit him more right now. Things like push ups, pull ups, walking lunges, ect. And getting him to train using resistance instead of weight. Those resistance bands would be perfect. And you can find tons of good and unique exercises for those bands on the net.
But yea, with just his own body and a resistance band, he can get himself on the track to build up his body.
And if losing weight is the issue, just getting him active will help with that.
The only issues with the gym is
1) Most the things in the gym he shouldn't be using yet anyways
2) It can be a fairly intimidating place for some adults, let alone a kid whos 12 lol. Unless he is with like an adult.
If your son needs somebody to help him along the way, then a trainer would be beneficial. Just make sure they know how to train a kid, because I have seen alot of trainers at gyms, train kids from 12-16 like they were adults. So, if you find a trainer, make sure he knows what he's doing and won't just throw your kid on some cookie cutter workout plan you can find in a magazine