Don’t give your kids an old box for gaming. That would be very frustrating for them. It’d be best to build one or two cheap (Intel) Wolfdale CPU-based systems (CPU, board, video and RAM). Look for a board with integrated video to save a few dollars. The Wolfdale systems (CPU + board) are inexpensive and can be aggressively overclocked. I have mine running at 4.9Ghz on 1150Mhz DDR2 RAM.
They are ages 5 and 2. By the time they are old enough to step up to a real system, I’ll have something else built. ;-)