As mentioned before brakes are not required for trailers under a gross weight of 750kg. If more than that you require brakes and a means of applying the brakes if the trailer come off the car ( a chain from the trailer brakes to car)
I would buy a lighting board to tie to the trailer (lights are the biggest problems with a trailer) and this is the simplest way to fix lighting problems.
Trailers must have mud guards, a number plate which corresponds to the towing vehicle.
Also worth having a spare wheel, wheel brace for the trailer and a jack which can be used on the trailer (check if the car jack will be suitable),
Securing the load is important, use ratchet straps etc.
Mike