But right up front, you should be aware that no matter how good your optics are, if the tube shimmies with the slightest breeze or touch, or picks up nearby footfalls, your instrument and your enjoyment will be severely compromised. So no matter which of the following mounts you decide upon, it should, above all, be sturdy. The decision of whether to go with an altazimuth or equatorial mount really depends on what you want to do with your telescope. Altazimuth mounts are easy to operate and less costly than equatorial mounts, and also are great for kids. You simply put the telescope on the mount and start observing.
Equatorial mounts are more involved.
The other, called the declination axis, is at right angles to the polar axis and pivots around it. These simply allow the user to move the telescope incrementally in either axis by manually turning a knob or cable. These come in handy when you want to make small adjustments to positioning an object in the field of view. Telescope manufacturers sell equatorial mounts with and without drive systems, although the more expensive models usually come equipped with one. It's not an absolute necessity otherwise.