Well a "G3" is an older processor type that was succeeded by the G4, then the G5, and now the Intel-based CPUs. An iBook is an Apple laptop that is somewhat smaller and less powerful than the Apple Powerbook laptops that would have been out at the same time. And then for the iMac... that's an "all-in-one" type of computer that has everything you need built into one unit.
For your budget, you probably are best off looking at either an iMac or perhaps a Powerbook. If you can get an iMac G5 for that kind of money, great. Most likely you'll have to settle for a G4 model though. The Powerbooks don't come with the G5 technology... so look for a Powerbook G4. Settle for no less than 512 MBs of RAM, but you should aim for a full 1GB or more, given what your son wants to do.
Now if you have a monitor and keyboard already, you could go with MacGirl's recommendation of the Mac Mini. A brand new one will have the Intel processor and give your son the option of dual-booting Windows if he really needs to (except for games, he really shouldn't need to).
I just did a brief eBay search, and you should be able to get an iMac G5 for about what your budget is, perhaps a little more. Unless your son has a need for a portable computer, then I would encourage you to go for either this or a new Mac Mini.