I'm running a set of BFG AT's, 285/65/18 on my 06 F-250 6.0 ltr Lariat stock wheels.
They are approx. 32.5". No issues at all.
33" tires would not be an issue on your stock wheels.
I just picked up a nice used set of factory 20's, as I am planning on selling my current setup, so I'm in the tire shopping mode as well!
From what I gather 12.5" x 35" tires will fit, but if your loaded heavy and turning tight you may rub in the front.
I want to go with the above size tires, so I am thinking about installing the 2.5" leveling kit that was mentioned above. It's just a simple spacer that goes in the two front springs.
Good luck with your tire shopping.