This is a common question so here is a very basic guide to choosing a size of guitar to suit your child:

4-6 years-of-age: either a 1/4-size guitar - or even a soprano or tenor size ukulele

6-8-years-of-age: a half-size guitar

8-12-years-of-age: a three-quarter-size guitar

12-years-of-age to adult: a full-size guitar

Of course children are not all the same so their height and the size of their hands and fingers will vary. The above details relate to the lower end of child size percentile. Always make the effort to visit a local music shop which stocks guitars of various sizes so your child can physically hold them and place fingers on their fingerboards. Some might disagree on this but I would recommend considering a small-for-age rather than large-for-age choice simply because any child struggling to reach the necessary frets to play even simple chords will usually lose interest in the instrument. 

As to the type of starter guitar to buy well, the general consensus tends to favour nylon ...