What size to buy for a child?

I want to purchase my daughter her first unicycle - she’s 11 and apx 4’2". I’m trying to determine which size would be best - 16", 18", 20"?

Also - what brand do you recommend for a novice? How much should I expect to spend?

16" and 18" are generally considered to be “grow out of” sizes, with little use beyond fitting small bodies. Your daughter should be able to fit on a 20", and that’s what I recommend if she can.

This one’s a great deal, as it comes with safety gear and a video (disclaimer: I appear briefly in the video):
http://www.unicycle.com/shopping/shopexd.asp?id=137

If your daughter does not have a 24" inseam, go with one of the smaller wheels.