Types
Telescopes fall into two categories: refractor and reflector. A refractor telescope has two or more lenses mounted within the tube. They are mounted in a straight line, so you have a direct line of vision to the object. A reflector telescope uses one curved mirror or a combination of mirrors. You see the reflection of the object through the telescope rather than the object itself.
A reflector telescope can enlarge the image more than the refractor can, but the image may be blurry around the edges. However, the right eyepiece can reduce that blur.
Mounts
Types of mounts include go-to mounts and clock drive mounts. The go-to mount allows you to enter the GPS coordinates of an object, and then the mount points the telescope toward that object. A clock drive mount tracks an object over an extended period of time.
The go-to mount makes finding specific objects in the night sky easier. The clock drive is preferred if you intend to use the telescope for astrophotography, as long exposures are required.
A mount, first and foremost, must be stable and sturdy; it is what you mount your telescope on for viewing. You also need to choose a mount that serves your personal preference, whether you prefer the go-to mount for its ease of use or the clock drive designed to work with your telescope for astrophotography.
Eyepieces
Purchase the highest quality eyepieces you can afford. Do not buy plastic ones, as they will not provide clear images. For backyard astronomers, eyepieces with focal lengths of 32 mm or 25 mm usually provide crisp, bright images.
Fixed or Portable?
The advantage of buying a telescope that remains in a fixed position is that you do not need to worry about acclimating to ambient temperatures or damaging the telescope in transit. The disadvantage is that you cannot take it with you to stargazing events or to any other locations from which you may wish to view the night sky.
Cost
Refractor telescopes are more costly than reflector telescopes, because they use lenses, which are more costly to manufacture than the mirrors used in reflector telescopes. A refractor telescope with a 5-inch lens may run as high as $3,000. A reflector telescope with a 6-inch mirror will retail for around $500.