jascht,
Upgrading is pretty straight forward. Of course, third party module can seize to work if not certified on the new version but in most cases it will not cause your whole site to malfunction - just the pages or modules in it.
So, upgrading... first, kudos to you! - You backed up! - This is a great start.
Second, since you are working on a production server, make sure you do this when there is least traffic on the site (mostly at night is good time).
What I usually do (and mainly because I run a pretty straight-forward unmodified DNN), is delete all DNN related folders on the Web server, with the exception of the DesktopModules, bin, and Portals folders. Primarily because they contain files that may not be in the new DNN - i.e. Skins, 3rd Modules, 3rd Party Module dlls etc.
I then update the new Web.Config file with my database settings - oh, please please please do not forget to copy over your encryption keys from your original file - or no one will be able to log in to your site, including ADMIN and HOST.
Now, upload the new files - do not worry about overwriting the old files.
You should be able to now open your site and upgrade with no problems.
If you still run into issues after this, email me directly - I'll help you out.