35's will generally give you a big enough sidewall either way. If you're buying new wheels, IMHO wouldn't go larger than 18", but 20" will certainly work fine. I have stock 20's on my '14 Mega but will replace with 18" when I replace the tires.
I wouldn't associate the word "handling" with a 35" tall tire as you are also generally going to install some type of lift to get them to fit. How well the truck will "handle" will be determined by how/what you lift to get there, overall tire height and width, etc.
As very general statments, less sidewall will handle better (less flex) on the road. Less sidewall will ride rougher (less flex). Less sidewall is less desirable off-road.
You do want to match rim width to tire width to minimize ballooning of the tire. 35x12.5x20, I'd recommend a 10" wide wheel for example. I wouldn't recommend putting anything much wider on a 10" wheel. Can you though, yes. I have 35x15.5x15 on a 15x10 wheel on my '74 K5, not recommended.
It sounds like it's primarily a pavement pounder, so I'd do whatever you prefer to look at.