Looking at different tire sizes?

I am looking into putting bigger tires on my chevy 1500. There is no lift on it and it's a 2x4. Stock size is 235/75/15 and I'm looking at 31x10.5's or 32x11.5. I'm pretty confident the 31's will fit and won't rub in the front. Does anyone else know if the 32's will fit on a 1500 without a lift or wheel spacers? And because the suspension should only drop the body as much as it did with the old tires; since the new ones are 3" taller that means the body should sit 3" taller (respectively) too right? I'm just debating if the bigger tires are worth it. I actually found a cheaper set of 32's than every set of 31's I've seen for sale.