If you are planning on carrying the trailer often (e. g. stairs to your apartment) it should be as light as possible.
If not already attached, a separate rear light according to traffic regulations ( depending on local legislation) needs to be added to the trailer. Tip: Buy a rear light with a rechargeable battery (available in stores from approx. 20 euros, as of July 2018).
The bicycle trailer should have a rainproof outer material and, if possible, a seal indicating the use of non-toxic materials in the upholstery and belts. The side windows and the top should have UV protection. Information on this usually is found directly on the demonstration models in specialist shops.
The prices for bicycle trailers range from 150 euros to approximately 1,400 euros (as of July 2018); the price range is comparable to that of strollers. Cheaper models usually are cheaply manufactured might be less convenient to use and often lacksuspension. Expensive, high quality trailers usually have good (and well-adjustable) suspension, have technical tricks that make them easier to be handled and/or are made in Europe. However, fundamentally, cheaper bike trailers are just as suitable for taking a baby along, provided that an adequate baby seat is installed. Bicycle trailers usually have a long durability and are often used by a family for many years, which relativizes the costs of purchase. There is also a market for used trailers. Here you might find an affordable model or be able to resell your trailer after the kids have grown out of it.