Probably just 31s. On my old cherokee i had 33s with a 3 inch lift BUT i also trimmed the fenders. I still rubbed at full lock though.

so with just the 3 inch lift i would go with 31s max without trimming.

here is a pic of my old jeep
1st pic 235/75/15 on 3 inch lift


2nd and 3rd pic.. 3 inch lift and 31s and trimmed fenders



4th pic is 33s with 3 inch lift and trimmed fenders

 

Looks like Silver Lake in the 2nd and 3rd pic! Used to love "Test Hill" in my buddy's Bronco!!

 

How much faith do you have in that rear 'tube' bumper?

 

I dont have that Jeep anymore, but it was straight when i put it on there, I got stuck and had to get yanked out very hard, and it bent it like that. the tube was welded on, and it was very solid. I pulled many people out with it like that (no recovery points)
My new jeep has front and rear recovery points so that is a plus