I bought my son a 3/4 scale guitar with nylon strings when he was 5 or 6.
That gave him enough interest to start learning, then I let him use one of my cheap full scale acoustics with steel strings at age 8 as his hands were big enough.
Currently he has taken up bass, so he is learning on a 5 string that my bass player had spare.
It is a challenge as he is only 11, but he is gaining hand strength and stretch.
The core for me at the start was letting him enjoy what he was doing, so nylon strings meant it didn't hurt his fingers.
Once he had decided he wanted to learn, he was mentally in a place where toughening his fingers up on steel strings wasn't an issue.
music.stackexchange.com/users/104/Doktor Mayhem
I started playing guitar at about 7 years old, I got a classical guitar, slightly smaller than the common size -but very slightly (I think it was larger that the '3/4 size', I actually played until I was 20!).
The important thing for a child, I'd say, is that the guitar is confortable to play: rather low action and normal-to-low tension strings.
Nylon, of course.
music.stackexchange.com/users/460/leonbloy
Consider a ukulele.
"Real" ukuleles are available cheaply (although you can spend a lot on a really lovely one).
It suits small hands.
It has nylon strings
so it's not too difficult to fret.
There are plenty of resources for learning real songs to play on the uke.
Having fewer strings makes for easier chord shapes.
It's a great instrument on which a child can learn the basics of fretting, strumming and plucking without having to deal with a large instrument.
One down side is that if he migrates to a guitar, he'll have to learn new shapes, to account for the extra two strings.
But to mitigate that, being adaptable to new tunings is a good skill -- and young minds adapt quickly.
And of course, he could choose to stay with the uke... or the mandolin... or the banjo... or any number of other guitar-like instruments.
If you do this, do get a uke book (or learn uke yourself, and teach him).
The high-tuned bottom string is counter-intuitive, so he'll need reassurance -- or with the right strings you can tune it low
so it feels more like a guitar.
Whether you go for a guitar, a uke, or something else, make sure the instrument has acceptable intonation.
Playing an instrument with bad intonation is really no fun whatever your standard.
If you do go for a steel strung instrument, pay special attention to the action and the string tension.
You don't want to put him off by giving him an instrument that's a struggle to fret.
music.stackexchange.com/users/1252/slim
I'm not (really) a guitar player, but I have taught beginners as part of a generalist music-lesson gig.
The other answers so far are good, but I would add two essential things from my own experience: The fretboard needs to be in tune.
Otherwise, the instrument is going to sound really bad.
If you're not sure, tune any string with an electronic chromatic tuner, then play the same string on each fret individually and notice what the tuner says.
If the guitar gets way off pitch, quickly, stay away.
It needs to be possible to set up the guitar so that the open strings (or strings when pressed down) do not arbitrarily buzz against frets.
Trying the exercise from item #1 on all the strings and noticing if there is any buzz (that comes from something other than improper finger placement) is a good way to check for this, since there is no guarantee that the frets are the same height all the way across the fretboard.
I remember teaching a very young student who clearly had a "toy" guitar, and these two issues made it almost impossible to teach her.
It was frustrating for the student and for me, and the student never really improved very much.
music.stackexchange.com/users/15/Andrew
I agree on quality.
You wouldn't want to give a child a pre-war Martin unless you're crazy and rich or he's Chris Thile in the making, but you wouldn't want to give something that pretended to be an instrument, either.
Smaller, but not too small, or else
the child will rightfully think it's just a toy.
Two crucial things to note: If the child is interested in playing electric, no acoustic guitar will do, and if the child is interested in playing acoustic, no electric guitar will do.
And your child, as with anyone who hasn't been taught to know better, will not know how hard to fret, and will thus oversqueeze, hurting fingertips (which makes playing uncomfortable) and pulling sharp (which makes the sound uncomfortable).
Early on, teach a light touch, and this will make the rest of the process easier.
music.stackexchange.com/users/195/Dave Jacoby
This is around the same age I started playing guitar.
The guitar I started on was my dads first guitar which was from the early 60s, it was a catalog guitar nothing fancy.
For strings, since I had an electric I had light gauge steel strings..
The way I got hooked was just by listening to the music my dad liked, which is the same music I like now and then..
I wanted to be able to play that music that I heard.
Just don't force it on him, thats is what killed it for me for about a year, yes try to get him to practice but make it fun not stern and dull, make achievements for him where he could get some sort of reward related to guitar .. like a strap that he saw that he liked, or something simple like that Hope this can be of some help for you.
music.stackexchange.com/users/2426/Joe W
I would go against buying a toy guitar.
This really kills everything from the start.
Rather paying a little extra might pay a lot in the long run.
For the guitar priority one should be, going for something that suits his body shape.
Something he is comfortable with it.
Also go for steel string not Nylon!
music.stackexchange.com/users/158/Quazi Irfan
We are looking for a guitar for my son, and have seen cheap ones at Toys R Us, et al.  He is just starting out, and we are trying to gauge his interest before spending too much.  Would it be worth starting off with what is essentially a toy, and upgrading later? If not, what things should we look for?  Nylon or steel strings? What size? 30", 1/2, 3/4? Is there anything else that would help him use the instrument?
What qualities of a guitar should I seek for an 8 year old?
music.stackexchange.com
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music.stackexchange.com/questions/4821
music.stackexchange.com/users/1610/Don
For a child's first guitar a smaller size of a real guitar is a better option than a toy. It should be comfortable for the child to play and have nylon rather than metal strings.  The answer to this question will be subjective, but you should probably avoid getting a 'toy' guitar. The most important thing will be that it is an appropriate size for your son and that it is reasonable enough quality to play without going out of tune too easily. There is no clear answer as to whether nylon strings are the best choice or not.
The most important thing will be that the guitar is a suitable size for your son. Quality is important, and the guitar should sound correct and not go out of tune too quickly. There is no clear answer as to whether nylon strings are a good choice or not. You should probably avoid getting a toy guitar.