Usually the most common type you’ll see on modified trucks are 315, 35” and 37” however they are usually paired with 17” rims or 18” which is more rare than 17, this is because you can fit a larger sidewall tire with smaller rims.
As for tire types and brands, I have a purely offroad focused car, so I have experience with Cooper AT3 XLT, and BFG KO2. These have worked great for me with a slight reduction in drive comfort which isnt a concern of mine anyway. I can vouch for these two, however other members of the club will be able to give more options based on their knowledge.
If you want to look rims, I would suggest Method as they have beadgrip technology, I usually run 11 psi, (and have went down to 5 when stuck) and never had a popout even on intense drives, but again, there are many different brands to choose from. (You should also look into the details such as what kind of offset you want to have.)
But if you do decide to go for big tires make sure they wont rub against your fenders/fender liners, remember bigger tires add more weight, and will put a bit more stress on your truck.
There are many factors which will determine the ideal tire and rim types/size for you such as whether you daily drive your truck and what your specific needs are. I have just suggested a few things based on my own experience. Tires and rims are quite a vast topic and you have alot of options to choose from .