Telescopes have two main attributes: aperture and focal length.
Aperture describes the diameter of the telescope's primary objective. This is the size of the primary mirror in a reflecting telescope, and the size of the primary lens in a refracting telescope. The larger the aperture, the more light the telescope collects and the greater the resolving power.
Focal length is a measure of the distance from the primary objective to the telescope's focal point. Telescopes with shorter focal lengths have wider field of views than longer focal length telescopes. Longer focal length telescopes provide more magnification.
Deja vu right?
If you read last month's Beginner's Question then you've read all that before. That discussion applies here too.
In general, for planetary viewing, you want high magnification, which means a long focal length and plenty of aperture. 8" Schmidt-Cassegrains and larger (aka. SCTs) are a good choice here.
Deep sky objects (aka. DSOs) include small and dim planetary nebula and galaxies, large reflection/emission nebula and open clusters, and let's not forget globular clusters and double stars. In general, small dim objects benefit from longer focal lengths while large objects are best viewed with wide-field of views (shorter focal lengths). Large aperture short focal length Dobsonians, and fast high quality refractors, are popular options for deep sky viewing.
In order to split close double stars, or to see detail on the planets, a scope needs to have the necessary resolving power. Resolution is often calculated using Dawe's Limit. This calculation is where a derived constant is divided by the telescope's aperture to get an estimate of its resolution expressed in seconds of arc. The main thing to take away from this formula is that the bigger the aperture, the better the resolving power.
Welcome to aperture fever. It's said that the best telescope is the one you use the most. This tends to be inversely proportional to the telescope's aperture and serves as a cure for The Fever. The larger the aperture, the heavier the telescope will be, the studier, and more massive, the mount needs to be. The larger the aperture, the more space it takes to store the telescope. The larger the aperture, the more cumbersome it is to transport. Of course, the larger the aperture, the more you'll see. Everything is a trade-off.
Astrophotography is another cure for aperture fever. By taking lots of exposures and using software to stack the images, you can see things with smaller scopes that you wouldn't be able to see viewing through the eyepiece. Most telescopes work for astrophotography, but Dobsonians tend to be a poor choice since they're usually on mounts that don't track the sky. When it comes to astrophotography the telescope optics aren't nearly as important as the mount. You need to take exposures of several minutes so it's critical that the mount track the sky as smoothly as possible.
There's no one perfect telescope, and most scopes can reveal tons of solar system and deep sky objects. For a beginner wanting to learn the sky, I'd recommend an 8" Dobsonian. If that size is too big, a 4.5" or 6" model are good choices too. If you want to get into astrophotography, use the scope you have, but if you don't have one yet, then consider a low cost 80mm doublet refractor for getting started, and use the savings to buy a nice motor driven equatorial mount with GOTO capability.