I have a little experience with trailers, we own 4 of them.
First get your tape measure and measure the outside to outside width of the front tires. Custom tires are wider than stock and rims have different offsets. A 16 ft should work since the SS is about 13 ft. long. However if you want more room an 18 ft would do that. I would recommend the 16 though.
Trailer Mfg's use different measurements, for example some V nose are measured from where the V nose starts others include the extra space. You can use that space to put junk in but not the nose of the sling.
I have an Alumina tilt 18 ft to haul our slings and Vette around on it is open. The only reason I went 18 ft was for the cars. I wouldn't recommend this trailer.
I would get a 16 foot V nose double axle if I had to do it again.
There are basically two types of enclosed trailers a cargo or a car hauler. The car hauler normally has the rear end that is angled down (dove tail) this helps but in most cases you may need extra ramps because the front end is so low it will drag on the ramp which is not long enough to avoid this The ramp should be heavy duty.
Tie downs. If you get a car hauler it will probably come with tie downs in the floor. You can see these in the picture above, or if you custom order you can pic where they go. Trailer floors are 3/4 inch plywood, if the tie downs like those above are just held in place by 4 screws good luck. One of the best ways to tie down is E track .It is held down by many screws and offers you a choice of how and where you tie to the SS. Foe example on the A frame or over the tire with a net.
One company that can make any tie down strap you need is MAC Tie downs, look them up on the internet, you can always use the cheap ass ones from Walmart.
Single or double axle. I would go double for two reasons. You can carry more weight and if your load is not balanced they do not swerve as bad . 7,000 lb. for the axles are ok you can go 10,000 if you want, extra cost, higher registration fees, larger tires. Keep in mind these trailers will come with electric brakes which will require your jap truck to have the connector for them and the control unit inside the cab.
As I said I would go enclosed. I know the SS is waterproof but the first thing you don't need to do at an event is look for a car wash or spend an hour cleaning it. They are not dirt proof.
Their are many options you can get which will make your life easier, most dealers can help you out.
Jamesgn