Not sure if the 1963 Valiant has the same rear wheel wells as the 1965 Barracuda. This is a tire that fits. Its a 275/60 15 on 1980's Cop Car Ralleys and V dog dish hub caps. A 235/70 15 does fit better.
I have not thought much about it yet but I was going to upgrade from the 13" wheels it originally had to 14x 5.5 in BBP. I was planning to use P205/75/R14 tires but I haven't thought about it yet.