You need to add up boat weight, motor weight, equipment and fuel/water that you plan on carrying. Then add in a 15 to 20% fudge factor. Or..Using an online trailer selection tool, I get a recommended capacity of 9500 lbs for a 200 GW 265 express.
Three axel trailers can be more sensitive to set up and harder to handle on the road. If you are not trailering full tanks and a ton of gear, the 2 axle seems to be OK.
All that aside, you need to decide on material (aluminum or steel), lights, brakes, rollers or bunks etc. I would go with disks, aluminum frame, LED lights bunks or rollers depending on where you launch.
5200# trailer axles are standard equipment on dual axle trailers, which are usually conservatively rated as 10,000# trailers. Whether that would be enough for your boat is another question. If it isn't, you're looking at a 3 axle trailer.
I have the same boat and bought a 3 axle trailer and havent looked back. Withe this setup you are right on the edge of needing a 3x. If you trailer alot go 3x. I love the ride. Also got E/H brakes, what a dream. Just don't get a brakerite system.