I had already guessed that I should get the Core so about three hours and twenty minutes ago I downloaded it and started it. It's just about at twelve percent. Should I shut it down, uninstall it and reinstall it, then open Armory?
None of that is necessary. All you need to do is wait for it to finish. I have used Armory while Bitcoin Core was already running before.
My "don't launch it" notice is just for convenience, so you don't have to open Core every time you want to use Armory, but it works just as well if it's already open, as it only uses it for the RPC calls.