Kid bike/trailer advice

I'm about to get my 5 year old her first two-wheeler (she's had some motor delays, now caught up, so we haven't rushed). I'm looking on advice for finding a good quality, but not necessarily new, sturdy two-wheeler for a very small five year old (weighs less than 35 pounds). Also, I want to get some version of used trailer/tandem that lets me hook her bike to mine. I've learned of the availability of a used Nashbar Trail Gator and a Trek Mt. Train 206 in the area. But I want to know more about safety issues, things to look for (or avoid), and also what kind of kids bike is best suited to this use. My own bike is an old but trusty Univega hybrid, fairly heavy with good fat tires. Terrain is flat.

Thanks,

Susan