Biggest tire in 64 barracuda stock configuration
I have 195/65 15s on the front of my '65. They look as tall as I would want to go. On the back, 225/60 15s should be easy. Another FABO member has 235/65 15s on the rear of his '66. He does have a slight rub.
Let me know if you would like a pic.
Good luck.