The other criteria I'd look for is flat protection. For one, you are probably pretty used to avoiding sharp stuff with your bike tires, but your trailer tires don't follow that same path (and you can't see the trailer tires) so you are much more likely to run things over with your trailer. In addition, emptying your cargo or kid on the side of the road to fix a trailer flat is really not fun!

As for efficiency, start with smoother. Knobs are a killer. After that, I'd suggest wider and softer for trailers.