Welcome, I see that you are fairly new on the forum. Tires are an ongoing topic here. You could use the search function and read tire threads for two week straight way hours a day.
Or, you could read and follow jimnlin advice above. He has towed commercially for many years with pickups and flat bed trailers plus tows a trailer similar in size and weight as yours.
I also have a similar size trailer that had junk chinese LT tires OEM and got them off in late winter of 2004-05. I install one of the tires he talks about, the Michelin XPS RIBs. I ran those for 6.5 years and 40K+ miles, and removed them based on age, as they still had 60-65 tread left. I sold them of Craigslist for 200 bucks and installed Bridgestone Duravis R250's. These two tires are the gold standard for trailer up to 6K GAWR.
If you are going to travel the country with your new rig, then that is the best. If you are going to just travel locally and shorter distances than a poly carcass LT will be ok. However the two I have used have a much better tread pattern for trailer use. If I was going to install a poly carcass LT it would most likely be the Firestone Transforce HT, as it is a lot of tire for a really good price.
Now, you need to go measure center to center on your axles. If you have 33" or more, then get LT235/85R16E's. If less than 33" get LT245/75R16E's and make sure you have enough room for a tire that is slightly wider.
If for some reason you feel compelled to buy ST (Spercial Trailer) tires, then get Goodyear Marathons, as Goodyear will pay to fix your trailer when they fail in a year to 3 or 4.
Someone may be along to tell you that if your trailer came with ST tires that you are required to use those in the future! At that point start using the search feature and study motives! You will most likely figure it out! Or PM members like jimnlin and myself.
Chris