Nice buy! How large are you looking to go on the tires? If you’re looking to replace the wheels I recommend aftermarket 17” wheels. You’ll gain extra tire on the sidewall. You can look at OEM 5th gen wheels or aftermarket. Aftermarket wheels will generally be lighter and have a 0 or negative offset. That type of offset will reduce the possibility of a large tire rubbing by pushing it out away from things (just like a spacer). You may still need to trim some stuff, remove mudflats, and push the liner forward.
Tires can range from something a little bigger than stock like a 265/70/17 or about 31.5”. To 275/70/17 or 32”. Or a 255/70/17 which is also 32” but narrower and likely lighter than a 275 (lighter and better on gas). Or just go big and go 285/70/17 33” tire.
Some popular all terrain tires are BFG KO2, Falken Wildpeak A/T3W, Goodyear DuraTrac, Cooper AT3, and various others.
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On the topic of new tires. I'm about to start a build on a 2008 V8 limited, will be deleting the XREAS and RAS (not sure if either is currently working, but don't care since I'm replacing them regardless), and putting on a 3" spring lift (or as much spring as I can get, possibly augmenting with a little bit of spacer to get to a full 3").
Currently planning to go with a 33-34" tire, but trying to keep the width at or under 11". What I'm wondering is if the amount of sidewall on 18s at that size would be "enough" since it's basically the same sidewall height as 31s on 16" wheels. Would the extra 1/2 of sidewall from going down to R17s would be a significant difference? Since the brakes on the V8 limited are probably sized for towing 7k, I'm not sure if they'd fit inside of 16s so I'm not sure if that's even an option.