First I would look for a good, solid mounting that does not wobble. No matter how small the telescope is, it can still give you very exciting views of the heavens, the Moon and star clusters IF the mounting is not rickety. If you must buy a store-bought or department store telescope, throw the mounting it comes with away and make your own out of pipe and pipe fittings. You can usually test the telescope right there in the store to see just what kind of mounting it has.
Secondly, the optics must be of the highest quality you can afford. This is a difficult issue to handle because you have to trust what the manufacturer says, but there may be back issues of Consumer Reports available at the library that cover most popular brands. It is hard to test a telescope in a department store because the conditions are very different than night time viewing of unresolved stars. Poor optics will show star images as comet-like shapes at the edges of the field, or show them to have colored halos.
Third you will need a finder or 'guide' telescope which is a low-power 6x telescope with a wide field of view. This helps you point the telescope so that the object appears in the eyepiece field of view.
The better telescopes also come with accessories such as a selection of eyepieces, a barlow lens and perhaps a 'wedge' for observing the Sun. Do not use a 'solar filter' because these can crack and cause the telescope to focus a blast of sunlight on your retina that will burn a hole in it in a millisecond!