15". I would want as much weight rating options as possible.
I would think that you will be loaded up rolling down the road near your GVWR .
I would want a 2100# plus, rated tire . Having that weight margin might allow them to run cooler which is IMO, one of reasons why some people are having ST tire issues.
Look into the PSI rating of the rim , some 15" tires are rated at 65# some at 50# psi. I'm not a tire/wheel expert, so I'm not sure about the importance of the rim psi rating between 50-65#.
If you choose the 'LT' tire option that some people install, check into the rims width . I think the rims/wheels on the trailers you mention have a 5" or 5.5" width. I would question if LT tires in your weight rating would fit .