As a man who developed a robust musculature through weight training in his teenage years, I was on more or less on the caveman diet. I still like devouring 1# ribeye steaks, pork chops or shashlik (i.e., Russian shishkabob.) Kids need a lot of animal protein to grow - I wouldn't skimp on that, just to save a buck that you could easily afford otherwise.
A good exercise regimen is definitely beneficial; I always try to walk anywhere to get my 30 minutes of walking per day (which is super easy in Europe, but super hard in most places in America, since a lot of places have no safe sidewalks!)
But tell us, are you so cheap as to not pay for them to join kids' sports leagues? My sister laid out about $30K/yr for her kids to play in high quality leagues (that were so good the only way to find suitable competition was to go away on a 400 mile road trip!) Although since I was never a big "team player", I didn't join such leagues, I think for most kids, it's a big psychological development tool.