+1 for Terry, if you can find/afford it.
But don't discount all kids bike.
Yes, most of them are built like the department store bikes I warned against in step 1 of my buying guide, but not all of them are. Look for brand name bikes (Trek, Specialized, Fuji, Giant, etc) that make high quality adult bikes, that are sold in real bike shops. Look for one with 24" wheels (20 will be too small), and other than that, the guidelines on components, fit, gears, and frame material are all the same as they would be for an adult bike.
A trailer should be able to attach to pretty much any bike. I pull my trailer with my 20" wheeled folding bike. Although there are a lot of different hitch options, and this may not always be true, the more common hitch types are pretty simple and mostly universal.