Hmmm
Seems you would want a trailor style that would keep the wind of the stock for winter hauling if it was needed. Vet trip etc.
Trailor needs a TOP of some kind, bars, solid metal something, NO open tops. Some areas and places not even let you load with a open top trailor. All kind of reasons their bad and not one good reason to have a open top that i know of.
Make sure the ball latch and jack works smoothly.
Does the gate(s) latch smoothly or have they been warped or bent? Make sure you can pin or lock the gates latch !!!
Lots of stock trailors have a center gate or two. Their pretty handy to have.
Spare tire included? You need one and it needs to be easy to access with out getting in the livestock area.....
Two axles are a really good idea with livestock. Much safer for you and the stock if you have a flat or blowout.
Does all the lights work ? They can be fixed but its something to keep in mind.
Title come with it ? Not sure how that works in your state. Be sure to get a picture of the the driver license and of the seller. Phones are great tools

Trailors are easily stolen and its possible a previous owner was not the honest type. You do not want to be the one stuck with loosing a trailor due to bad paper work.
Rust is a issue on the inside from manure left in and not cleaned out. Salt and what not on the outside.
Tack area or a container to haul in your truck to put your ropes, leads, halters, blankets etc in when using the trailor. Water bucket and a bit of feed in another bucket is often handy to have.
A ramp on the back or LOW entry level is really good idea. Taller it is the harder it is to load em.
If its a goose neck make sure you can let the tailgate down and back up to the trailor and be able to go a bit to far and not bend the tailgate. Many gooseneck trailors have really short necks and its easy to bend your tailgate when hooking on. Especially if your backing up to them at a angle. Also on rough ground such as swales, terraces in the pasture you can bend the edge of the bed. Especially when turning fairly sharp. I prefer goosenecks though
Brakes work ? You need them.
Check the bearings by wiggling the tire. Any movement is not good. Grease them after you buy one if its used, and i know its silly but make sure theirs lots of grease in even a new one, its easy to pop off the axle caps and check. Be careful of the grease buddy type caps. Pumping in grease can blow out the seal in the back of the bearings.
Wet trailor beds can be darn slippery, what kind of bed does the trailor have? Metal beds have their pros and cons. Something to keep in mind. Rubber mats can be bought to solve the issue but that's more money and something else to take out and put back in when cleaning.
The aluminum idea is a really good one.
I am sure i be missing something but this should get you started.