If you're looking at enclosed trailers to haul a car, you need a minimum of 18' to fit the car and still have a little room around it so it does not rub. Typical trailers have a 6' door height - If your vehicle is taller You can order many trailers in 6" taller increments until you have sufficient clearance. Remember the taller and longer the wall, the more it will catch side winds.
You will be able to store things along the side as long as they are well secured, but anything wider than 1' will have to be in front, behind, or inside the car.
You will want an escape door on the side of the trailer so you can get out of the vehicle once you pull into the trailer - This door allows you to open the driver door instead of climbing out of the window or rear hatch.
I prefer wheel bonnet straps verses strapping down the frame. There are axle straps, but it can be hard to position them without damaging brake or electrical lines. Wheel straps can be cranked tightly keeping the wheels on the trailer floor so they do not move yet the vehicle can still be travel on the suspension while transporting it. Well placed recessed D-rings rated for at least 1/3 the maximum vehicle are better than using a track system although less flexible.
Most enclosed trailers will weigh close to 3000 lbs empty which gives you 4000 lbs of payload on a cheaper dual 3500 lb trailer. If you think you are close to that weight, get the heavier framed 10,000 lb trailer with 5200 lb axles.
I prefer torsion axles with a drop since each wheel can move independently, the center of gravity and load height is lower which also reduces the ramp angle. If you decide on a trailer longer than 20', consider not using drop axles because you will have height clearance issues with driveway curbs and even some speed bumps.
Your pusher may be rated for the tongue weight, but I added a WDH on my truck (I have double truss 2' extension to clear my camper rear). I have a friction sway bar I never mounted because my setup is stable without it. Part of the stability will be the quality and design of the trailer the rest will be your hitch setup.