Your application is the most important factor in choosing a microscope. What you need to see and what you want to do with that image will determine what kind of microscope you need. Microscopes typically come in two types: compound or stereo microscope.
The most common is the compound microscope. It is the one most people visualize when they think about microscopes. A microscope with one eyepiece is called a monocular microscope; with two eyepieces it is called a binocular microscope, or it might have an additional camera tube and is called a trinocular microscope. The compound microscope has a number of objectives (the lens closest to the object being viewed) of varying magnification mounted in a rotatable nosepiece. It uses a light source beneath the stage to illuminate slides. These microscopes are generally used to view very small objects such as cells or bacterium. Magnification of compound microscope scopes range from 40X up to 1000X. Actual magnification can be figured by multiplying the power of the eyepiece by the power of the objective lens.
The other type of microscope is called a stereo microscope or dissecting microscope. It uses two eyepieces and two paired objectives. Stereo microscopes come in models that have full zooming capability and models that just have only two magnification settings. Stereo microscopes are particularly useful for biologists performing dissections, technicians building or repairing circuit boards, paleontologists cleaning and examining fossils or any one who needs to work with their hands on small objects. You can find stereo microscopes that have a built in light source from above, below, or none at all. Magnification is usually much less than that of a compound microscope, but is figured in the same way by multiplying the power of the eyepiece by the power of the objective lens.