...Be forewarned...if you just want it for a toy, then go right ahead, buy that $19.95 discount store special, or even the $75 music store version, but if you are actually interested in a "real" guitar for your child to learn to play on, figure on spending an absolute minimum of $175 to $200, and if you truly want a decent instrument, you are looking at a couple of hundred more! If you do buy a good one, though, its resale value is very good. People are always looking for *good* half-size and 3/4 size instruments, and you will likely have no trouble at all selling it for at least what you paid for it.
Spending that extra time and money now will pay off in that your child will get an instrument they can actually enjoy playing on, not just playing with. It can make the difference between igniting an interest and destroying one. We once bought a 3/4 size for our youngest, and though we knew it would not be a fine instrument by a long shot, we thought it would prove adequate for her to start out with. It only cost us a little over $70 including shipping. We wasted both the price and the shipping! We are now following our own advice and looking for a decent 3/4 size in the $300-$400 range.
To check one out:
1. Know that if you don't want to spend a lot of money, you are not going to get a lot of guitar. You are very unlikely to get an excellent instrument at a bargain price, but you may be able to find a very good instrument at a very good price if you take the time to look carefully.
2. Buy a "pitch pipe". It is a good, cheap investment, and a very good tool to have on hand when looking for a guitar. You will need it later anyway. (A friend who really knows stringed instruments is a good tool too, if you happen to have one handy.)
3. Hold the instrument so that you are looking down the neck of it from the peg-head (where the tuner keys are) to the sound hole, and be sure that the neck is straight - no twisting or 'scooped' look - you should see a flat, straight line all the way down the edge of the fingerboard. There should be no angle where the neck meets the body, it should just be a smooth flat continuation. Now try the other side.
4. Be sure that the strings are not too far up away from the neck - if they are hard to push down they will make the child's fingers sore and distort the sound. Conversely, if they are not high enough, they will rattle against the frets below.
5. The frets (the little lines of metal that go across the fingerboard (aka-fretboard) should be smooth - run your finger down the edge of the fingerboard on both sides - you should feel the bumps of the frets on top, but they should not stick out past the edge of the fingerboard, and there should be no sharp places.
6. You need to make sure that the strings will hold their tuning - that when it is tuned to standard pitch (A-440 - got that pitch pipe yet?), that the tuning stays - if the strings are constantly slipping out of tune, your child will be exceedingly frustrated. If you do not know how to tune a guitar, or don't have a pitch pipe, and are in a music store, have them tune it for you, and then plunk around on it for a few minutes and see if the sound changes. If the strings lose their tuned pitch quickly, you may find they will not hold at all later. Find a different instrument. Don't fall for the "Oh, it just needs tightening" ploy - if it 'just needs tightening', they should make it right before they put it on the sales floor.
You can get real guitars in half or three-quarter size for you child to learn to play on from most reputable dealers, but you still need to be sure to look for those check points above. The price doesn't tell you how good it is either..., and salespeople are after a sale, not necessarily your best interests.
It may be a good idea to ask for a short term trial period of a month at rental price before purchasing, but be prepared to put down a good sized deposit. Also, be sure that you and the store are clear on what the terms and conditions are before you do this - choose a reputable store!
NOTE: Be sure that you and your young musician take very good care of the instument. A guitar that has been used a lot in a month may not be in "perfect, unused condition" when returned, but should have no added scratches, dents, or gouges either. It is imperative that your child understand that this is their responsibility. Even if there is only a cardboard case, it is there for protection, and should be used to keep the instrument in when not in use. Caution should be used to be sure that other members of the household treat it with respect as well - no "borrowing", don't use it to hold up the play tent, and the cat shouldn't see it as a new scratching post either.