Cool. I basically did the same thing. I also picked up a new 2003 trailer with 3500# axles, 18' w/2' dovetail to go along with a F350 CC C&C.
Determine what the max weight tow capacity is for the F150. Figure out you planned to do when you wheel as well. How much gear you will be taking, how you are going to sleep overnight, camp, etc.? Then determine how you are going to pack it all in.
A simple topper on the back of the bed can be used for the overnight camping weekend wheeling trips. It may not be the most comfortable, but its off the ground and no tent to pitch in the dark when you arrive. The topper can be had cheap of CL.
Putting gear, tools, etc in a cargo box can be easily done with it on the trailer up front. A simple used truck tool chest/box off CL.
Camping gear can be placed in the bed inside the topper.
Need a long enough trailer to put storage box up front and the Jeep on it securely. Figure 2-3' of additional space front/rear of the Jeep for the straps. Triangulation is best to secure the Jeep when hauling.
Having a dovetail to the back of the trailer provides easier driving the Jeep onto the trailer when its running. You shouldn't need ramps. For non-running, you can pull the ramps. With a dovetail trailer, the ramps won't be as long and heavy as compared to a flatbed trailer with same deck height.
When looking for a trailer, figure out how the straps will be secured to the trailer. I had to weld in D-rings even though my trailer had the stake pockets and rub rail. The hardware for the straps is also very important. I use axle straps and 2" ratchet straps with hooks. My hooks were too big for the rub rail and stake pockets. I could have left the hook on the outside of the rail/pocket but it would have a tendency to slide and the strap webbing was against the edge of the rub rail. Topside D-rings took care of that.
A steel deck can be heavier than a wood deck. It all depends on the croosmembers underneath and deck thickness. I had a steel deck trailer but the cross members for the deck were just angle iron and the deck wasn't thick. I have a wood deck trailer now and it has 1/4 'C' channel crossmembers.
The tongue frame, trailer deck frame, and axles are important. My Jeep is small and light, so the 3500# axles with the 5on4.5 wheels is considered light weight for a trailer. However, the trailer has 5" beams for the tongue and trailer frame. So its a mixture of heavy framing and light weight axles/tires. The tires are Load Range C and that is the lightest I would go with a tandem axle setup. 1 has brakes. My upgrade for this trailer will be 5200# axles, 5on5 wheels (larger bearings/hub) or 8on6.5 wheels and LR E tires. Look out for used trailers with P rated tires. These are passenger car tires and even though have a capacity to carry the weight, they are not a trailer tire. The tongue also should extend past the trailer frame and go to the axles. There are many utility trailers that have an upper rail to them. The rail is necessary to keep it rigid. The tongue angles to the trailer frame and usually stops there. The outer trailer frame will be channel, but the crossmembers are usually angle iron. These trailers are light weight and I wouldn't consider them to be Jeep haulers.
The bulldog coupling is popular for heavy duty trailers and is easier to put on the ball. Although, it really doesn't matter which coupling you get, the other can have issues when there is road salt and debri in it.
Lastly, make sure you get a good rated tongue jack to lift the coupling off the ball with your Jeep and gear loaded.
Good luck on your search. I used CL and was happy with what I've found out there. Many sellers don't really know the technical terms of their trailer, so you may have to go visit them before you find one that meets your needs.
The steel deck trailer

Its crossmembers

Wood deck I kept



It now has a fullsize truck chest up front for storage of straps, chains, bottle jack, truck fluids, etc. I wanted to toss a side of a utility bed from a small pickup but I couldn't find one. Lots of fullsize utility bed (service box bed for pickup), but they are really too long. A small pickup would be great.