CURRENTLY A WORK IN PROGRESS
I suggest buying a simple instrument that is reasonably well made within the constraints of one's budget. I also strongly recommend that the guitar get a proper setup, even if this stretches the budget a little bit. A setup, where the string height is adjusted for best playing, the string length modified (where possible) so that chords sound more in tune, and the simple electrical and mechanical components of the guitar are checked and maintained is critical to learning, more so that buying a "better" guitar or a particular guitar.
If you are mechanically inclined and feel you want to learn how to do a setup yourself, the best resources are books or videos by Dan Erlewine or for acoustic guitar the web site Frets created by Frank Ford.
I find a great many people buying guitars for children or others with small hands who think that they need to purchase something special, a guitar with a narrower or thinner neck perhaps. Once one is dealing with at least adolescent-sized hands, I do not think this is necessary. The width and thickness of any common guitar neck will be manageable and a slightly wider than average neck can make some fingerings easier to execute cleanly and the resulting greater string separation in the playing area is an aid to learning most picking styles. If anything should be a concern for those buying for small hands it's the "scale length" which can range between 23 and 26 inches on popular models. Some chord forms are more difficult for small hands to stretch to with a longer scale length neck