Ubuntu has a built in backup tool (there are many others too), there is a good tutorial on how to do this on "How To Geek":
http://www.howtogeek.com/108869/how-to- ... th-dj-dup/
for simplicity I'd back up to a local storage place (USB HDD etc) but not
the drive that you are going to be installing over!
(Made this mistake once many moons ago...
) I am not sure how nicely Mints backup/restore tools play with Ubuntu One when it comes to restoring. When you have backed up remember where you put it, and once you have your Mint installation type "Backup" into the application search or equivalent. Give it your password, and then choose "Restore" from the options available then follow the tool through (steps such as telling it where your backup is kept and where to restore it to).
Hope this helps