The brake controller is definitely needed. It is not hard to install if you are a little familiar with electricity. It's also cheap to have done at auto shops if you don't want to fool with it.
One thing you'll find if you search through threads here is, every time someone posts their tractor and what trailer would be good for it, someone says "longer trailer is better." You can also find lots of threads where someone has sold a barely big enough trailer to get a longer one for weight distribution, or carrying more implements. But there's almost never a post like, "well, I bought this 20ft trailer and I sure wish I got a 16ft instead."
So basically, look at the price of something like an 8x20 equipment trailer, and compare to a "barely big enough" one, and that should give you an idea of which way you want to go. Will your tractor fit on a 16'? Sure, but not with much flexibility to move it forward or backward as-needed for weight distribution -- an important thing when towing with a 1/2 ton.
As far as weight capacity goes, a tandem 3500# axle will work for you. A tandem 5200# is probably over-kill unless you plan on carrying materials on the trailer or using it for other things. Again, though, the price difference is not really big.
I have a Gatormade trailer, which is a manufacturer in Somerset, KY, probably as close to you as they are to me. I am really happy with mine and I suggest you have a look at them. They are not the best quality, and I don't think anyone will tell you otherwise -- they are a medium-quality trailer at very good prices.
You need to think about if you want a beaver/dove tail or a flat tail-section of your trailer. Lots of threads on this. I have one beaver-tail and it's okay except you have to watch your ground clearance.
Ramps, slide-in or fold-up? Again, depends on what you want. Fold-up can get in your way, especially if you thought about letting a mower hang a little off the back or something.
A few things you definitely want if you order a new trailer, instead of find a used one or buy off-the-lot:
* LED lights
* fold-down jacks at the back will help you load, depending on your style of ramps
* stake pockets will make your trailer more useful
* factory installed D-rings are the best way to tie down equipment, and they are a cheap option
* if you might want a winch, think about having a 2" receiver put at the front so you can mount a portable one
* tool box for chains?
* spare tire and mount? radial tires or bias ply? plenty of threads about the difference
Also, I personally am not buying any more trailers with couplers other than the 2 5/16" size. I am tired of switching mounts. On the size trailers you are looking at, you will probably be 2 5/16" by default anyway.
I hope this helps. Look around at used stuff, but keep in mind that repairing something that isn't in good condition can be a real hassle. Also think about if you really need a trailer often enough to invest in one. If you are only going to move your tractor a few times a year, that's a lot of money to tie up in a trailer.