I'd go for guitar because it's versatile, easy to get a good sound out of, looks cool (very important for kids, a lot of the time), and portable. Also, you can, with a bit of searching, get one that sounds good but isn't too expensive, which makes it easier to bear if it gets broken or the kid loses interest.

My brother has a 3/4 size guitar, it's perfectly playable. It might be better to get a nylon-strung one for very young children, as steel strings can hurt the fingers and that's not exactly encouraging...and i'm sure kids' curiousity could lead to some pretty creative ways to injure themselves on steel strings...
One thing i think is important, is to get one where the distance between the frets hasn't been scaled down with the rest of the guitar, as this might get confusing if and when the person gets a full sized one.

Also, a good teacher is important, no matter what the instrument is. Doesn't matter if they're paid, or just a friend who can play... they have to be able to get the pupil interested, or the kid will just give up.