Really, any of the Shimano rear derailleurs are fine. I would wait until it breaks before replacing it (based on your description, you might be there already), and I would replace with another Tourney. They shift just fine. Any derailleur bent or damaged is not going to shift well. Until then, it should work very well. One problem/nuisance on any upgrade is I am assuming your son's bike does not have a frame mount for the RD, so it is a claw unit. Most the Tourney derailleurs have integral claws, whereas the better stuff, you will need to buy a claw to mount it.
On shifters, I can't stand the twist grip stuff myself. I have installed many sets of the Tourney push button shifters, come complete with cables and housings. Find them on line for $13. The only issue for some people is the front is friction, but I prefer friction on the front anyway. I have used dozens of these over the years, on several personal bikes.
http://www.amazon.com/Shimano-SL-TX3...8159623&sr=8-4