Online storage is a better choice than floppy. Go through this list and see if there isnt something you can use:
http://www.100best-free-web-space.com/
You can basically only backup files and not programs that are installed.
In internet explorer go to File>Import and Export and send your favorites someplace you can find them. You normally want to save these.
If you keep your e-mail on the computer, establish an online account with someone like Yahoo and foreword any mail you want to keep to the online account. You can export your address book so you can save it.
Go through Windows Explorer and find any files you want to save. Just download everything you want to save to online storage. If you dont have that much stuff to save you can put it on floppies just right click the file, Send To>Floppy A .