A basic smartphone can do almost anything you would need for recording your son at a baseball game, including live-streaming. You can buy accessories like mounts, tripods, handles and even gimbals to improve the recording quality. The only reason I can think to upgrade would be for optical zoom, which is much better than digit zoom if you're too far away from the action to get clear video. For that you need a camcorder or DSLR. You can get a decent Sony or Panasonic camcorder w optical zoom for less than $200. Those don't have too many modern features, just basic high quality video recording. Camcorders or DSLRs with lots of cool features like wifi (not for streaming) will cost at least $500 and realistically more like $1,000 and up.