The poster should visit a local astronomy club and try an Alt-Az mount and an equatorial mount and see what he likes. Everyone is right and everyone is wrong in this thread. Equatorial mounts are more expensive, but easier for a beginner to use under high magnification and somewhat educational (see the discussion on polar aligning). So (my $0.02) if you REALLY want to see PLANETS under high mag, then equatorial mount is the way to go, especially if you're going to be having several kids looking at the scope in turn. (Under high mag a planet can rotate out of the field of view in the time it takes one kid to leave and another to step up to the eyepiece.)
HOWEVER, the money you save with an Alt-Az mount could be spent on other things like a larger mirror more eyepieces or "digital setting circles". But the main diff is in what your target observation is. Most amateurs prefer "deep sky objects", Hercules cluster, Andromeda galaxy, Orion Nebula, low power (~50x) high light gathering (at least 6" mirror) is key here. The key to "tracking" is to think about how the earth rotates. Sun sets in the west so if you know where west is when you're looking in the eyepiece, you know which way to move the scope when the object moves out of the field of view. Not that complicated, but a bit like rubbing your tummy and patting your head at the same time. But to use a AltAz mount to its fullest potential, you should know how to read star charts and navigate to the various deep sky objects (or get digital setting circles).