Biggest tire I can run on a 1964 plymouth valiant

+1 on getting your brakes squared away before ordering rims. there are so many different flavors of rear disc kit that it's impossible to give a single answer.

figure out your brakes and then measure to confirm how much room you have, then select your rims. getting rims with more backspace than you need-- say an inch-- will allow you to dial it in using a spacer if need be.

with the constraints of the early body narrow wheel wells, it's critical to verify and measure, especially when going for max width.
I couldn't agree more. 100%correct.