Open Disk Utility. Select the drive entry from the sidebar. In the partition map displayed click on the partition in question. Set the format type to Mac OS Extended, Journaled from the dropdown menu. Click on the Option button and verify that the drive is using GUID then click on the OK button. Click on the Partition button. You should be OK for Time Machine.
I'm assuming this HDD is your startup drive? If it is, then you shouldn't use it for backups.
I know very few people who have trouble installing Ubuntu on any Intel Macs. And Snow Leopard is irrelevant because Linux is not installed in Snow Leopard but runs exclusively by itself.
If you plan a proper Linux installation then I would read the documentation and forum information at Ubuntu's website to learn what to do and how it's done. I don't know why you want to use Linux considering that OS X is a superior form of Unix which in turn is superior to Linux.