Aperture is the diameter of a telescope's lens, or primary mirror. The more aperture a telescope has, the more light it can collect, and the more you can see. This is important for deep space objects because they are so far away that they're very dim. The telescope collects enough light to make them visible to the human eye.

The focal length of a telescope is the length of the path that the light has to travel, from the lens, or primary mirror, to reach it's focal point (the point where it focuses to a bright little spot).

Longer focal lengths will provide more magnification per eyepiece, and provide a narrower field of view. However, you do not want to use a magnification that exceeds the resolving ability of the telescope. You can figure out how much magnification you can theoretically use by multiplying the aperture, in inches, times 50.

You can figure out the magnification that will be provided per eyepiece by dividing the telescope focal length by the eyepiece focal length.

Now that that's out of the way....

Telescopes that are used for terrestrial and astronomical viewing are typically refractors. I suppose it's because they're a lot more rugged that reflectors, and less cumbersome to transport such that they can be taken on hiking trails. However, these telescopes can't be used for serious all around astronomy. Because of their small aperture, they can't collect a lot of light and so are used primarily for lunar and planetary viewing, as well as astrophotography of star clusters.

When used for astronomical purposes, it's best to get an apochromatic, or at least an achromatic refractor to correct for chromatic aberration. The problem is, these are expensive. A small 80mm apochromatic refractor is $500.

Reflectors, and catadioptrics like Schmidt Cassegrains, are not very well suited for terrestrial viewing because they are typically of fairly large aperture so collect a lot of light, are more fragile when being transported. They are best suited for serious astronomical viewing. That doesn't mean you can't look at ground based objects with them though. You will want a special attachment to flip the image right side up though.

I suggest you buy some good binoculars to look ar your view. You can beat using two eyes. You can mount them on a tripod to steady them. For astronomy, if b y star gazing you mean you want to look it vast star fields, with room for planets, nebulas, and galaxies, I'd get a richest field telescope. This will be a reflector with a focal ratio of less then f/6. For example f/5

For astronomical purposes, I wouldn't get a telescope smaller than 4.5"

You can go here to learn more about telescopes:
http://members.aol.com/siriusbc/telescopes.htm