Hi Paul,
The two main specifications of a scope are the objective lens (OG - expressed in millimetres) and the magnification (expressed in X). OG's generally range from 50 - 80, with 50 being small, and 80 being large. The bigger the objective, assuming the scopes are equal in terms of optics, the brighter the image. This also means they can support higher powers. 50mm scopes have advanced, but to get the best out of them, a magnification from 20-30X is best. A 60-70mm scope is often seen as the best compromise, as it still collects alot of light, can support good powers, and are usually still compact and small.
Magnification, the higher the magnification, the duller the image. Most scopes come without an eyepiece - and it is the eyepiece that defines the magnification. A typical magnification that is useful for almost any situation is the 20-30X range. There are two types - a fixed eyepiece, aka a wide angle, and a zoom eyepiece. Fixed e/p's give a set magnification, so are less versatile than zooms, which will give a variable magnification - usually 20-60X. However, while the zoom is more versatile, a fixed eyepiece - especially at the lower end of the market - will give a sharper view, with a wider field of view. Field of view (FOV) is a measure of how much 'stuff' you can see through your scope, and the lower the magnification, generally the more you can see through your scope. At the top end of spotting scopes though, the zooms are very sharp, but not as wide as a fixed eyepiece. A good zoom is an expensive eyepiece. FOV is expressed in the UK as the amount of metres you can see through the scope at 1000m. A wide eyepiece is usually ~40m. Good zooms are usually (depending on magnification) 35ish to 20ish.
Other specs are weight - ~1kg is a lightweight scope, coatings - what the optics are coated with - they improve light transmission - look for fully multi coated optics, and ED/FL/APO glass. This glass is an expensive element that improves colour correction, reduces purple fringing and makes the image sharper.
Perhaps you could give an indication of budget so we can give suggestions.