Half size is probably too small. The only thing to think about is that a 9 year old will grow out of a 3/4 size guitar probably within a year, but a full size is too big right now. Also, it does depend which type of guitar you end up getting. Traditionally kids just get a nylon string guitar (classical type), and most shops will recommend this, I however do NOT! I get angry about this a lot. These days a cheap electric guitar not only is easier to play for kids, but obviously looks cooler, and is cooler. There's always a thing with people saying in the 'olden' days they learnt on a piece of crap guitar and it didnt do them any harm, well thats good but a hell of a lot of students dont want the struggle on a guitar thats hard to play, and these days guitar has a lot of competition- videos games etc. In the 60's,70's and 80's you just get a good cheap guitar that was anything but hard to play, you can now, which is great.