Now that you've chosen the trailer that will best suit your needs. You've taken all those points into consideration, it's time to shop. Here is a list of things to check when purchasing your trailer whether you are going through a dealer or a private sale.
1.) If you are going through a dealer, make sure it's a reputable dealer. Better business reports and reputation.
2.) Check that tires are new and not worn and that you have the proper size spare tire.
3.) Check that there is a break away battery and that it's new or recently replaced.
4.) Make sure that electric brakes of the trailer are in proper working order and don't buy a trailer to haul horses in without trailer brakes.
5.) The trailer should have running lights and all lights, brake and turn signals are in fine working order.
6.) Check the floor of the trailer. Some trailers have wood, others aluminum or steel. You don't want rotting wood floors or rusting metal ones. Also check that planking of wood floors is supported well and spaced close together (ie: too wide=dangerous)
7.) You want all doors/hatches to open and close with ease. It's good if the trailer hinges and latches have been maintained with silicone grease ( helps to reduce rust ).
8.) A clean title, just like buying a car.
9.) Make sure you have the correct size ball for the trailer hitch, even a gooseneck. And heavy chains to connect from trailer to vehicle.
10.) Think about what you may need to replace or add to your trailer (ie: rubber mats, reflectors, reflecting tape, water source, feeders and hay bags).
Once again, I invite anyone out there to add their advice. A trailer is a matter of personal choice. The most important thing to think about is the safe travel of your precious cargo.