Summer is a time when students take a break and get busy with other activities. Children can take summer classes in singing, dancing, martial arts, painting, piano, voice lessons, and guitars. If your child wants to learn the latter, it is important that you get a guitar that he can easily handle, otherwise he might give up if he is uncomfortable using a big guitar. At this stage, guitar size is more important than a full tone.
For very small kids, a ½ size guitar is a safe bet. Older kids would be better with a ¾ size guitar. For teens, guitars from O to Om would be perfect. Cutaways are not necessary, unless he will use the upper frets. I only recommend dreadnoughts for beginners if your child is tall.
There are cheap guitars that are locally available for less than US$50. Be warned though that these are made of cheap plywood or lawanit. It may not even have a truss rod for adjusting the neck. If your budget is low, find one that has a very low action (strings are close to the fret wires) for easy playing. Chances are you cannot adjust the action on these guitars. Do not expect these guitars to have a good tone, but they may be good for beginners who may give up after a few sessions. If you have the budget, guitars starting from US$100 would be a better choice.
Here is an article on my search for an acoustic guitar for my ten-year-old son.