What is the highest OS I can use on early 2008 Mac Pro?

Pre-Installed MacOS:

X 10.5.1 (9B2117)

Maximum MacOS:

X 10.11.x*

from:

https://everymac.com/systems/apple/mac_pro/specs/mac-pro-eight-core-3.2-2008-spe cs.html

10.11 El Capitan.

The download link in the article below will work ONLY with a Mac that cannot run Sierra.

How to download OS X El Capitan - Apple Support

Note that for responsive operation, MORE than 4GB RAM is required for El Capitan and later -- still more for video or photo editing. It is quite true that Apple says you need 2GB to Install. But they do not say that performance with so little RAM will be acceptable. (it won't be.)

Your Mac can install, boot, and run from ANY appropriate drive, internal or external.

It would be prudent to be certain you have a Trusted Backup at a minimum, and some would suggest installing on a different drive, in case you need to go back or tie up some loose ends using the old system.

I'm going to guess El Capitan. I think that's why you see many people selling that generation Mac Pro these days. To answer this kind of question I usually have a look at everymac.com specifications since they include what is possible now vs. Apple's pages which usually state what was originally possible.

It looks like you will be fine with RAM.

You can certainly install another Rotating drive or SSD. Many Macs are I/O bound. If you are doing editing, one of the next-biggest speedups is having your source and destination on different drives, and having both be a different drive from the Boot drive.

Time Machine is a good backup system. "Trusted Backup" is a term I use to describe a system that seems solid and YOU trust. We always hope we will not need it.

If you were going BACK to a previous system, I would suggest you make a second Backup, in case the first fails you. But for going forward, or using a different drive, that is not necessary, as you will not need to ERASE your drive to do this upgrade.