An Amiga 600 makes a great little gaming machine for the kids. My friend has an A2000 with only 3MB RAM, but it's filled with WHDLoad and other HD installed games and is awesome, so you don't always need an A1200.
Make sure you get them some newer (non-AGA) games like Fightin' Spirit, Stardust, Ruff n Tumble, Mr. Nutz, Project X, Superfrog and not just the really old games that most people can only remember.
Sure AGA is nicer and the A1200 is faster, but the poor little A600 would feel neglected and I bet the kids woud think it's cuter, and might not even notice the graphical or speed differences between the ECS and AGA Amigas.
You could use Magic Workbench or one of the other more colourful icon packages from Aminet, combined with a good colour palette (use Full Palette from Aminet to lock the colours) and then you can resize and remap any pictures you want with Personal Paint.
Or if you wanted another great option, you could get a CD32. Nearly every WHDLoad game will run on them, and the ones that need keyboards are being patched to use the extra buttons on the control pad, and of course there are heaps of awesome CD32 games too.
