For the OP, The limiting factor is the Load Range E requirement.
First you must start with a tire of the correct size and Load Range E, after meeting that requirement you then look for tread design and tread compound.
If the bulk of your use is on the highway pulling a trailer, I would look towards a highway rib design for the tread over an All-terrain type.
Finding a good Load Range E tire of that large size for under $200 is going to be a challenge.