You should make a backup copy of all your files and settings and store them all in some other media before you do any work on your computer's hard disk. Most people now have too much stuff to fit on DVDs, so either a USB flash memory stick or another hard drive will likely be needed, you can use a USB external hard drive if you want. I think that's what most people probably use these days.

If you want you should be able to resize your existing Ubuntu partition smaller to make room for your new Ubuntu installation and have two Ubuntus in the same hard disk. You can do that either with GParted in the Ubuntu CD or with the installer's partitioner during the installation process. Install a new Ubuntu beside your old one and then copy your files across. You still should make a files backup in another disk beforehand though, to be safe.

EDIT: Also, have you read this sticky: Graphics Resolution- Upgrade /Blank Screen after reboot ?