I recently ordered some new parts to upgrade/replace my backend. It all came in today. I want to get it up and running and from what I understand I can just install a fresh copy on the new computer and then backup the old machine, restore on the new one and then copy the actual recorded files over.

One question I have is if I should put it all together today or wait until the new version drops and install that copy. I just am not sure if I will have issues restoring everything from my old backend. Any advice?

My own preference is for clean installs rather than upgrades, but that's just me.
For future reference, keeping an extra hard drive on the shelf with the last older distro of KnoppMyth on it, will give you something to use for checking out 'the new computer' quickly.