They put "P" rated tires on there because they have a softer sidewall and thus a softer ride with 20" wheels. Im sure the tire is rated to carry whatever the weight of the fully loaded truck is, otherwise they wouldn't be on there.
"LT" rated tires have a stiffer (higher ply) sidewall. You will noticed an increased stiffness to the ride as well as handling.
As for gearing, doesn't matter what size the wheel is as long as the overall mounted diameter of the tire is the same as the OEM equiped one. Furthermore, you would have to make a big change in the overall diameter to make much of a difference in the gearing. Adding or subtracting 1/2 inch to 1 inch on the overall tire diameter wont matter much, even to your spedo that will be off at the most 2 MPH. If you go up in diameter, it will show slower than actuall speed, if you go down in diameter, it will show faster that actuall speed. It will effect you odometer as well.
Go somewhere like tire rack and enter the truck info, then select a tire and wheel package. They should only show what is listed as OEM sizes / combos for your truck.
I would ALWAYS put LT rated tires on a truck used to carry heavy loads and tow.