It's promising that it shows up, that model can run 10.6 & can update to the latest OS if you want.
With regards to backup, you will only be sorry if something goes wrong.
Personally I backup a lot, especially before upgrading any OS. Normally it is fine, but if something does go wrong all you have is regret and a mess to try to fix.
There are a few options for backup, Time Machine is OK if you understand the limitations - basically it copies the system, your user files & keeps older copies of them. Eventually the older copies are deleted when the disk space runs out - depends on how much data you have & how much space the backup disk has. This format means it isn't bootable. If you need to restore you have to install a working OS & then use Migration Assistant to move the data from the backup - it's pretty simple & pretty reliable. You can also pluck files out if required.
Another option is to make a bootable clone, either via Disk Utility (built in, made by Apple and is free) or via an app like Carbon Copy Cloner (free demo, if you pay you can schedule copies to be automated) or SuperDuper!. This can also be restored to the Mac, either by reversing the clone operation or by using Migration Assistant. This type of backup generally has no history, it;s a fixed point in time, but it is normally an option to keep some history in the paid for apps.
http://bombich.com/
http://shirtpocket.com/
How far are you planning on updating? If you are going up to the latest OS you may want to make a clone of each intermediate stage.
It may sound complex, but it's not too bad considering you data is less likely to disappear in the event of an error.
Do you have any external disks that are large enough to contain a copy of your Mac? The backup process will normally require the disk to be empty.