Over the past year I've migrated my Linux systems for the kids from Ubuntu to Xubuntu and now to Crunchbang. It's a fantastic, no-nonsense system for getting stuff done. It can play games, especially web-based ones. It uses a Debian base similar to Ubuntu. Most importantly, it seems to go fast. There's little in the way of eye candy or nifty desktop tricks like wobbly windows. Instead you have a minimalist desktop (actually 2 virtual desktops, but I reduce it to a single desktop to prevent confusion for the Pre-K user) with a simple menu. I have it running on systems as old as an Asus EEE laptop (the really old kind with the 4GB SSD).
Something to think about for your current (slow) computer if you're planning on upgrading to a new computer in the near future.