1. backup the entire DB
Meaning: Control Panel, Backup, All Tables, right?

2. copy all files over to the new server from the old one
FTP from old server to new.

3. if you are changing domains or the new server paths are different, you will need to edit the config.inc.php to reflect that
Same domain, different server (new IP address)

4. import the DB into your NEW server
Just not sure what that means....

...and verify current _non_ upgraded version is still running
I'll have more questions once I get to this point.

5. then upload the 7.5.6 new stuff (only files required as in the readme) -- including install directory
Wait.... do you mean I should install into a 7.5.3 setup, THEN upgrade? If that is the case, I guess that explains Gizmo's suggestion. I think I'd rather install to a 7.5.3 setup and THEN upgrade. Is there any advantage to upgrading the old forum first? (I'd rather keep it running smoothly while I hack away in private.)

6. run install/upgrade.php
Does this step read the backup files I created in step 1 and import the data into the db tables?

I REALLY do appreciate all the help. Since I only dabble in this, I am really green.