The first question you should ask before buying a microscope is, "What do I want to observe?" This determines the type of microscopes you need, as well as how to prepare the subject for observation.
Very small subjects - cells and microorganisms - require a lot of magnification and you will need to prepare a glass slide to observe them. The slide is then used with a compound light microscope at magnifications anywhere from 40x all the way up to a maximum of 1500x, depending on the subject. The compound light microscope is the most familiar type of microscope and the one people think of when you mention the word "microscope". This is the microscope we first used in science class. A glass slide with the specimen is placed on the microscope stage and is first viewed at low magnification, then at higher magnifications by rotating a nosepiece which has 3 or 4 objective lenses attached.
Compound vs. Stereo Microscopes
A compound microscope produces images that are upside down and reversed right to left and the working space between the slide and the lens is very small. For this reason, it is not practical to work on specimens while you observe with a compound microscope, nor can you fit large subjects under this type of microscope for observation.
Large subjects - twigs, rocks, leaves, flowers, gems, industrial parts and so on, don't require the magnification of a compound light microscope, but they do require much more room under the microscope to observe them. The type of microscope used to study these subjects is called a stereo microscope or sometimes a dissecting microscope, since you can observe the specimen and cut it or operate on it at the same time. The stereo microscope is widely used in science, industry and is also a favorite of hobbyists.
Although not as well known as the compound microscope, a stereo microscope is a great choice as a beginner's microscope. You can put just about anything under it - a backyard is full of interesting subjects - and there are no slides to prepare. It's also the most user friendly type of microscope since images are upright and correct right to left, just as seen without a microscope. Magnifications are low, so focusing is not as critical as it is in the higher magnification compound microscope.