A ramp. Ample tie down points. Tires with the proper load range for the heaviest load you anticipate hauling. Interior lighting for those times when you have to load in the dark.

Ramp back door for sure.

Side door also is nice for camping in it using a roll screen.

Make sure you get white. A black trailer heats up to 300 degrees in the summer sun. You can also paint the roof with Sno-coat (like a school bus) to reflect away the heat.

Buy a good lock for when you park it, people always steal them off your property while you are at work. A Kryptonite "New York" lock can't be cut with bolt cutters or broken with a bottle jack.

A hitch dolly makes quick work of backing it into some tight spot that your truck might not want to go without jackknifing.

If you buy a used one, repack the wheel bearings, because there will not be any grease in them.

bumping this up as I'm in a similar situation. Don't have a pinhauler (not planning on getting one) and renting a uhaul trailer each time. Granted it's only 15-18 per rental, but it would be nice not to have to pick up/drop off and planning it all out.

Anyone haul pins in a utility trailer? In bad weather? I would imagine lots of plastic wrap, tarps and tie downs...

Just make sure you buy a spare tire/rim at HF, because you will be totally screwed if you blow a tire and don't have the spare.

Regardless of where you are storing the trailer, look at into buying a GPS tracker and installing it in an inconspicuous place. Never know when someone may decide they need the trailer more than you do.

For enclosed, roof clearance is important.
Dual axel is preferable if your going to haul a lot of machines at once (but not crucial).
Its also a lot more stable if you have a blow out at higher speed.

Things like anchoring points for tie downs are important, but can always be added if it doesn't have sufficient.
As others have mentioned if it doesn't have a spare tire, buy one.
Ive had a couple blow outs on game hauls, mainly during the summer out here when the roads are hot as hell.

I also have a lockable tool chest bolted to the front of mine.
Its great for stowing your ratchet straps, spare bulbs, jack, wheel chock, or other things you might need.
I also keep a spare socket wrench and basic tools in there like a set of screw drivers in the event I run off in a hurry and forget them.

Here's mine...

http://www.jeff-z.com/dodgeram/haulmark/haulmark.html

I've had it for about 14 years. Great for pins and no more uhaul.

I've toyed with the idea of buying an enclosed trailer but never pulled the trigger. I gave up renting the smaller one-axle trailers from uhaul because they basically had no suspension. Both times I rented the 5x8 I had damage to the pinball machines I was transporting. Those trailers are total crap especially over potholes or bumps with any kind of speed. I have since always rented the bigger 2-axle trailers and they seem to ride a lot smoother. The two axles are a lot less maneuverable.

Looking at purchasing new trailers, I lean toward dual axle for the smoother ride and less sway. I've seen some nice single axle trailers that appear to have decent suspension on them and some that don't. If I was buying a single axle, I'd pay attention to how much travel the suspension has and maybe invest in a shock kit.

Depending on your tow vehicle buy as big as you can afford. I went from a 5x8 single axel to a 7x16 v nose tandem axel. Both trailers have roughly the same effect on my mpg. The tandem axels make the ride much nicer and the electric brakes take the worry out of stopping in traffic. Most trailers are manufactured in southern Georgia and I saved about 1k by buying direct and picking up the trailer from the factory. I installed e track on both walls making securing pins much easier. I can easily load 10 pins into the new trailer. I also built a nice bar with mini fridge in the v nose section. Found some bug screening for both doors and now I also have a kick ass trailer to camp out at music festivals. The dog loves it too....

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I have the same exact trailer as yours even the color, mine has a 7ft ramp opening for very easy loading of pins or UTV.

That's a sweet looking trailer. Does the place you got it from have a website?