Steve,
I hope this is not to boring, but these are some of my thoughts and opinions. I like enclosed trailers for long distance towing when going to races as you can put all your tools, etc in the trailer. My philosophy is out of sight out of mind. It gives me peace of mind when staying in a hotel overnight and I am pretty fussy where I park it when at a hotel. I don't put any lettering or names on the trailer. IMO you are just asking for it to be broken into if the less desirable know what is in it, and in certain states it is an invitation to be pulled over by the highway patrol for being a commercial vehicle, and that can be a real headache. Also an enclosed trailer is nice to have around the house just for vehicle storage in the off season as you can pull the motor out of the vehicle and then put the vehicle back in the trailer. It is also nice at the races to have a place to get out of the elements, wind, rain etc.
I would go with a 10,000 lb GVW or more with two 5200 lb axles with brakes on both axles. Your enclosed trailer will weigh in at around 5000 lbs depending on length unless it is made of aluminum, and that only leaves you with putting 5000 lbs in it.
My current trailer is a 34 foot Featherlite aluminum gooseneck with two 7000 lb torsion bar axles equals 14,000 lbs gross. It weighs about 5000 empty, has 26 foot of floor space with 8 over the bed. One of my cars weighs 5000 lbs. so with this trailer I can put in an additional 4000 lbs before being overloaded. I like springs better than the torsion bars but that is just my preference, and this trailer came with torsion bars. I also like having a gooseneck for safety purposes, and 8 lug wheels. I use a 1 ton truck to pull with.
In the end it just comes down to your preference, your tow vehicle and how much your car weighs with all the stuff you take to the races. If you have a very light car and don't take much to the races you can get by with less trailer and less tow vehicle, but heavy race vehicles need HD trailers. Remember how much time and money you have invested in your race vehicle, then buy a trailer and tow vehicle accordingly. Or you will be telling horror stories on how many tires you blew, bearings you burnt up, etc. Most people unknowingly overload their trailers and pay the price.
Tom G.