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 ...

When you first start playing acoustic guitar you may find it hard to get a good sound from it, especially if you are a beginner with soft fingertips. The notes you play will often sound dull and rather stilted and the music doesn't flow nicely. So think about the sound you are creating as you play, try to make at least some of the longer notes sound "sweet", using your fretting finger to add a vibrato effect to the sound. Classical guitarists typically do this by moving their fretting fingers back and forth along the length of the strings whereas blues, rock and electric guitar players tend to bend them by moving them from side to side. It helps if you have access to a recording device of some kind so you can frequently record and listen to yourself playing as you develop the technique. Becoming emotionally involved in the music you play will have a profound effect on your desire to create the variety and quality of sounds which the guitar is so capable of producing. So don't hold back!