The mount is the half of a telescope that nobody photographs and everybody underestimates. A perfect optical tube on a poor mount is unusable at high magnification, and the cheapest way to ruin an otherwise good instrument is to hang it on something that shakes when you touch it.
Alt-azimuth, the simple kind
Two axes, up and across, exactly like a camera tripod head. Intuitive, cheap, and quick to set up because nothing needs aligning. The drawback is that following an object across the sky needs both axes moving at once at continuously varying rates, which is why undriven alt-azimuth mounts do not track and driven ones need a computer to do it.
Equatorial, the tilted kind
One axis is tilted to point at the celestial pole, so a single steady rotation follows the sky. That makes tracking mechanically simple and is why every long exposure photograph before the computer age was taken on one. The costs are weight, counterweights, a polar alignment step at the start of each session, and a learning curve that puts beginners off.
What to spend where
A rule that holds across the shelf: if the budget will not carry both a good tube and a good mount, buy the smaller tube. A dobsonian base is the cheapest steady mount in existence, which is why the design dominates value, and a 130mm dobsonian at $305.00 will out-observe a 90mm refractor on a wobbly equatorial costing the same money.
The settling test
The one test worth doing in a shop or at home: tap the eyepiece end at high magnification and count how long the image takes to settle. Under two seconds is good, over five makes focusing miserable, and that single number tells you more about how much you will enjoy the instrument than any optical specification on the box.
Questions people ask about telescope
What types of telescope mounts are there?
Alt-azimuth, which moves up and across; equatorial, which has one axis aligned to the pole so a single motion tracks; and computerised versions of both, which find objects as well as follow them.
Which telescope mount is best?
For visual use, whichever is steady for the money, which usually means a dobsonian base. For photography, an equatorial, because tracking accuracy is the limiting factor rather than the optics.
Why does my telescope shake?
Almost always the mount or the tripod rather than the tube. Spreading the legs wider, lowering the height and hanging a weight from the centre column all help noticeably.