Need help please

[64 4x4]

Hey guys,
I just bought my dream truck. A 1964 chevy k10 4x4. It has the original 292 engine and transmission. All of the front fenders(they have small rust spot that was patched with a big ugly stainless plate...),hood, bed, etc. are original. Just missing the trim and not original paint. I am going to put new tires and rims on it (31's are too small for me). I was wondering if anyone knew the max tire size I can fit under her without shaving the fenders or rubbing. My dad has the same year truck but his is a k20 and he has 35's on his. I would like to go bigger then that. Also does anyone know if there are any lifts available? If not any suggestion on getting her up higher would be great. Pictures included(big blue is my dads. Pic is from when we picked it up where he bought it from).