The first piece of gear we got was your basic 2-child trailer. This would have been in 2005 when our oldest daughter was 1. This is a Schwinn, bought at a local big box store for around $160, if I recall correctly. This picture shows it with its "stroller" handle attached. We never used it that way, but I'm sure would do the job well.
There were (and still are) other options made by manufacturers who specialize in bike trailers (like Burley), but they cost considerably more. There are also cheaper options. After pulling this for hundreds of miles, many of those miles with friends pulling a smaller and cheaper trailer, I'm glad I spent the money on this one, and don't feel like I needed a more expensive one. The large wheels (16 inch) roll more easily than the 12 inch (or smaller) wheels common on many other trailers, and they use standard quick-release levers to attach, which makes it easy to break it down to go in the trunk of a car. This trailer also has a fair amount of storage space behind the seat, which we put to good use more than once on some longer trips.
The trailer after being folded for transport or storage.
The trailer hitch that goes on the bike looks like this (picture borrowed from Amazon without permission):
We bought an extra one so both parents' bikes so the trailer could be switched between us easily. The small hole in the hitch attaches to the rear axle of the bike. It adds probably 2-3 mm of additional stuff that have to fit inside the nut or quick release skewer. One of our bikes required a longer quick release skewer in order to make it fit, but I happened to have an old one. The other bike (a Giant OCR3 from about 2005 or so) has a rear dropout that looks like this:
I don't have experience pulling other trailers, so it's hard to say how pulling this trailer compares to anything else. The one thing that took some getting used to was that it really forces you to pedal smoothly. There's enough flex in the hitch mechanism and the long bar that attaches to the bike from the side of the trailer that any hard acceleration feels like pulling on a bungee cord and wastes energy. This is probably the case for most trailers that mount on one side (as opposed to some cargo trailers which attach to both sides of the rear axle of the bike).
I never required my children to wear helmets in this trailer, in part because we just hadn't bought them yet at the time. I can say from experience that these trailers are extremely stable, and would be difficult to knock over (I have crashed once while pulling this trailer and it remained upright). This is a fairly roomy trailer, and it worked well for our kids up to the age of about 4. By the time our oldest was 5, it was getting clear that she just didn't fit, so we took the next step and bought a trailer bike, which will be my next blog entry.