Time machine should happily back up to a partition on an external disk, as long as you've formatted it for a Mac filesystem. Don't even think about trying to get it to use a Windows NT or DOS or Linux partition 
Btw, things to think about:
- Maybe encrypt the backup. Time machine can save to an encrypted backup, but you have to set it up that way when you start the backups, not after you've been using it for a while. Consider the panic of having your backup drive stolen.
- You can easily exclude directories in time machine so you don't waste time/space backing up files you can easily recreate from other sources.
- You can have multiple backup drives and it'll round-robin the backups. Disks fail, even backup disks.
- Many external disks are bus-powered and small enough to easily fit in a bank safe-deposit box. Consider a small fire (or flood) in the room that houses both your computer and backup disks. Consider occasional swapping with an offsite. Or copy the most important files into the cloud as well as time machine.
One other word of advice I'd have is to have time machine show it's status in the system menu bar, and try and avoid sleeping or powering off the machine if it's in the middle of a backup. Also there's a "feature" where you can only easily trigger a backup (Back Up Now) via the time machine system menu.
Humor: I still miss my 8mm Exabyte tape drive. 2Gig on a cheap tape. Pretty cool for the day.
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