I'm amazed at the "stick with P rated oem" posts. I have to suspect these are folks with limited towing experience.
P may be fine to tow a popup with a minivan, but once you move into real TVs and towing anything of size, LTs are the way to go.
You will also notice the significant difference in tread depth with an LT, which can be quite a benefit when pulling a trailer in and out of a grassy spot.
LTs give you the option of a higher ply rating of 6 ply or 10 ply. This rating can be thought of as a resistance to puncture or split. The sidewalls are stiffer, the hauling rating is higher.
So the definitive recommendation is yes, absolutely LT, unless you plan to once a year for about 20 miles and always stay on blacktop.
The options would be 6 or 10 ply, E rated or not, upsize or not, whatever your preference.
P tires are oem to make a truck ride like a car. Going to use it like a car, then stay with Ps. But if you plan to tow, haul things, leave the blacktop (gasp), and actually use the truck (or SUV) as a truck, then get some real truck tires on it ;)
Of course, you are free to do as you please, but this is the straight dope about changing the tires.
Hope this helps.
