OS 10.4.11 portable hard drive question

I have been a loyal Mac user since 1986, but am not a major techie. I have Tiger OS 10.4.11 and now find it's incompatible with things I need to do since I need to upgrade my browser and this OS won't run the new browsers.... So... I need to upgrade to Snow Leopard. In order to do that, I will want a portable hard drive to backup my system before I switch so I can do a clean install...
I've done a lot of research and am pretty much leaning towards a Seagate Backup Plus for Mac but I'm not sure if it will run with Tiger 10.4.11.... Anyone know if this will work, and if not, do you have a suggestion for a hard drive that will work with Tiger and will also work well with Snow Leopard?
Thanks for any help you can offer...
PS After looking around at many forums and reviews, I'm working hard to avoid Lion which sounds like a disaster I'd rather not pay megabucks to experience! (I had thought about just getting a new or refurb Macbook Pro, but they are all shipping with Lion and I"m told you can't "downgrade" to snow leopard! :-( )

The drive will work just fine, its just a drive after all

AS for the Seagate software that comes with it, not sure, but I would just reformat the drive for mac and let SuperDuper clone your old Macs drive

Snow leopard will then ask for for a backup drive when it finishes and you can restore your stuff from the backup

SuperDuper!

Thank you, thank you, thank you! Your answer has exactly the info I need to finally solve this issue that was beginning to seem unsolvable. Checked out Super Duper and it sounds like the perfect solution to my back up needs till I get snow leopard installed.

Yep. Don't bother with any of the software that comes with the drive. Just use Superduper or Carbon Copy Cloner to clone your Mac as a bootable drive.