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 ...

A good question, especially since the web is overflowing with instructional articles and videos to the point that it almost seems like everything these days can be had for nothing!

Well, although they say you really only get what you pay for, I'll be the first to admit there are some pretty good guides available which do indeed cost zip. So if you happen to be one of those rare people who can follow an on-screen tutorial and diligently work through it from beginning to end until you wind up playing the example piece brilliantly, then indeed you may not need the services of a guitar teacher at all. As for the rest of the world well, most people do need the discipline of working under one-on-one guidance if they are ever to achieve anything like the goal they set themselves. That is just how it is. Even the super-gifted people mentioned earlier who can soak up the odd YouTube how-to movie, well, even many of them will likely admit there still remain certain aspects to playing a piece ...