From the PIF, a PW with winch is 5,950 to 6,000 pounds for easy figuring. That is empty weight nothing else whatsoever.
I own a 20' Gooseneck Tandem Axle, rated at 12,000 pounds. I ordered it with 14,000 running gear which gave me larger brakes and tires and more steel in the frame. My wheels are standard 8 lug and I can swap spare tires between my Ram and trailer. I have electric brakes on all wheels that are controlled ny a Jordan full proportional controller. I have 83 inches between the fenders. With STA Super Lug Tires, I have plenty of room. If your going to run Larger tires, you will need to get a full top deck so you have full width.
A 10,000 pound rated trailer will just barely squeak by with a PW. As an example, my 20' Gooseneck weighs 3600#. Its rated for 12,000# which gives me a 8400# load. If You had a 10,000 rated trailer that weighed 3000 you would only have a 7000 # load - 6000 for the PW and you have 1000# extra for stuff.
I would only suggest a 12,000# rated Tandem axle/brakes on all wheels as minimum. Don't skimp on a trailer, there is a lot of JUNK out there and for a few bucks more you can get a quality trailer. My Gooseneck is a Corn Pro, made in Indiana. I feel its loaded with quality. www.cornpro.com My Model is the Heavy Duty UT-20 20' Gooseneck.
I also use Grade 80 DOT transport rated chains and ratchet binders at each wheel and 4 lighter chains and binders at each corner to stop any wallow on the springs. I want my load not to move on the trailer. How to tie down can almost become a religious war. LOL
And you must have a Tow Truck capable of the weight your hauling.
My Ram 2500 CTD, two people, Gooseneck and my Carryall is a GCVW
Gross Combination Vehicle Weight if 18,500 on the road. Nothing less than a 3/4 ton truck set up for hauling and much better is a 1 ton.
Finally, If you haul with a Gooseneck, you will never look at a draw bar pulled trailer again (except for small trailers) the handling is fantastic.