Refracting telescopes use an objective lens to gather light.
There are also catadioptric telescopes that use a combination of lenses and mirrors.
All telescope designs use an additional lens (eyepiece) to focus the light into an image.
Below, in the sources section, I have posted a link to a useful guide to buying telescopes on the Sky and Telescope website. If you want to get a good idea of what you would want, I highly recommend reading it. It's long but informative.
I personally have a Newtonian reflecting telescope. It's objective lens only has a 5 inch diameter, so it has its limitations. It was still pretty good for observing the moon, planets, the Orion Nebula and star clusters.
For a good all around telescope that would give me more satisfactory resolving power, my astronomy professor recommended a telescope with a mirror of at least eight inches. However, as the aperture (objective lens/mirror diameter) gets larger, the telescope gets more expensive. If you want a large aperture than a reflecting telescope would probably be best choice. It is also important to note that the quality of the lens/mirror is also important for the resolution as well.
If you are a true beginner, I wouldn't recommend getting anything too complex and expensive. My five inch Newtonian has kept me satisfied for a decent amount of time.