Alt-azimuth mounts are very easy to use, telescopes can be moved up and down or left and right. Larger telescopes usually mounted on dobsonian mounts which is much more easy to transport than an equatorial mount. These mounts can be used for daytime observations as well.
Equatorial mounts are usually used with astronomical telescopes. The biggest advanate is that one axis is parallel to the rotational axis of the Earth and thus as they're easily capable to track celestial objects.
The GoTo mounts can find the selected targets in the sky automatically. The hand controller stores many thousands of objects, thus after selecting one the mount can turn the telescope to the proper direction. GoTo mounts are usually manufactured with higher accurancy and are recommended for astrophotography.
These motors can be mounted on equatorial mounts and work as a clock drive by default. Using a GoTo kit the mount can be upgraded to a fully GoTo capable one.
Mounts can be powered from different sources: rechargeable batteries or different adaptors.
All accessories for the mounts can be found here: polar scopes, dovetails, counterweights. Accessories for astrophotography can be found under "astrophotography" menu.