i just went through all of this. It was brutal i spent a couple days at the parts store with the guy trying to figure out how this was going to work and what was instock. To run 37x13.5 your best to go with a 20in wheel with at the very most a 5in backspace. Now that all depends on whether the tire is actually 13.5, i found a lot of them if you look at the specs are closer to 14. I personally went with super swamper m16's 37x13.5r20 and the wheels have a 4.5in back space and a -12 offset. The way the tires stick out looks awesome its not to far but not sucked in to much. The only rubbing issue i had was the plastic stone gaurd on the driver side rocker panel rubbed a bit so i trimmed it back a bit. The only time it rubbed was when the wheel was turned half way i was braking and pulling into a store with a roadside curb. So not really a big deal but still an issue. What ever you do dont go with 35's. I find they just look way to small, even the 37's dont look that big on there. As far as the lifts go i went with the skyjacker and the guy who install it was extremely impressed, even the alignment was barely out after. It keeps all factory geometery and the ride height is level where as a lot of lifts still leave the front sagged down. I did a hell of a lot of research on the lifts and it came down to procomp superlift and skyjacker. All seemed to be in close quality but in the end personally the skyjacker won hands down.
Hope that helps
I have an 8" lift total and I am running 37x12.50x20 and I have plenty of room.I am going to a 37x13.50 next time.I have pics all over this site of my truck.I have it in the Gallery too.if you can't find a pic of my truck holla and i will post one here for you.