It is important to choose an instrument that is set up properly and is the correct size for your child. I recall several occasions when a new student arrived for a first lesson with an instrument that was too big or of  poor quality. Two common problems that are easy to spot are pegs that don't fit properly and a poorly formed bridge. The first results in the instrument not staying in tune and the second ensures that the quality and volume of sound production will leave something to be desired.

Doing a little research before purchasing an instrument for your child will pay off in the end. You can get advice and second opinions from experts such as luthiers, fine instrument dealers, specialized teachers, and articles like the one below.  When an instrument is the correct size and works properly, everyone involved - you, your child, and the teacher - will get much more enjoyment from lessons. Most importantly, there will be a greater chance your child will want to stick with the instrument.

http://www.stringsmagazine.com/cello-instruments/Cello-Instruments.asp