Try making a simple text editor similar to edit.com from the old days of DOS, but with a twist; multiple file editing at once. Hope that helps. :)

Regarding Ubuntu's live environment, if your machine has about one gigabyte of RAM, it should be able to run. With 12.04 LTS, I won't vouch for smoothness, but it should do ok. No matter which distro you use, burn it on a CD so you can free up your USB ports for any external storage you're wanting to use in order to back up the data you're wanting.

I will warn you that Zorin would probably not work as it is not compiled for the ARM architecture. You'll probably be better off using a distro listed on this page here. The link points towards downloads of the distros already supported as well as instructions for installation. I believe Fedora 17 will also be available if it isn't already. Just remember that the Raspberry Pi uses the ARM architecture as opposed to x86.