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.
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.
Features You Should Look For:
A. Compound microscope
Beware! You can achieve any magnification by simply combining the right eyepiece with the right objective, but this does not mean you will be able to effectively use the magnification produced. It's a matter of optical quality. Most beginner microscopes under $200 do not have enough optical quality to effectively use magnifications over 400x and most inexpensive models under $100 do not have enough optical quality to effectively use even 200x at best and much less at worst, despite manufacturer's claims to the contrary. (One very good exception is the LOMO P-111, by the way. Easily the best buy in a beginner microscope on today's market!) Just as importantly, it is much more difficult to use a microscope at high magnifications than at low magnifications. For a beginner, 200x is more than adequate for viewing cells and pond water microorganisms, anyway.
Any microscope designed for practical use will have two focusers, a coarse focus for low and medium magnifications and a fine focus for use with high magnifications. This is because focusing at high magnifications is more difficult and it requires a finer touch. A single focusing mechanism is a sign of a cheap microscope and it makes it very difficult to use high magnifications, even when available.
There two basic light systems used in a beginners microscope: mirror and built in illumination via a 110V power source. (The little LED lights advertised on inexpensive microscopes do not count, as these are too feeble, even when they do work.) Mirrors will work by placing the microscope near a sunlit window or by adding an external light source via a desk lamp. A built-in light, though, is much more convenient and is also more effective to use at higher magnifications. It is a feature worth spending more money to get.
The most detail is not necessarily seen under the brightest light and some organisms, in pond water, for instance, are light shy. Inexpensive microscopes have no way to adjust the light, but any useable scope will. The simplest mechanism is called a diaphragm with holes of various sizes located under the stage. Better microscopes use an iris mechanism, similar to what is used on a camera lens. This allows for much finer adjustments.
You will need something to hold the slide in place, especially at high magnification, where even touching the slide may be enough to move the specimen out of the field of view. Two types of holders are used. Stage clips are the simplest and least expensive and they will work, though they are nowhere as convenient and easy to use a mechanical stage which has fine control knobs for moving the slide right to left and up and down.
Monocular and Binocular Heads
Using one eye for any length of time produces eye fatigue, since you are straining the focusing muscles on your observing eye differently than your resting eye. Serious microscopes offer a head with two eyepieces which not only reduces eye fatigue, but also increases visual acuity.
Oil Immersion Objectives
When light passes from the glass surface of the slide to the air above the slide, some image quality is lost. When that light then passes from the air above the slide into the glass of the objective, image quality is lost again. An oil immersion objective uses a drop of oil between the slide and the objective which has the same refractive (light bending property) as glass and thus no image quality is lost. It's as if the slide and the objective were made into a single piece of glass with no air between. This type of objective is an essential tool for serious, high magnification observing of very small microorganisms such as bacteria, but it is typically not a feature needed by a beginner. It's a viable option to add to a microscope at a later date, but only if the microscope has the optical quality to handle such magnification.
B. Stereo Microscope Features
These are low magnification microscopes, typically between 10x and 40x. More magnification is not needed or desired, because as magnification goes up, field of view goes down, so you see less and less of the subject and as magnification goes up, depth perception decreases as well. This can cause problems when trying to manipulate the subject. It is still fascinating, though, to view ordinary objects, even at these low microscope magnifications. They appear much different through the eyes of a stereo microscope.
The least expensive stereo scopes have a fixed magnification, typically just 20x or just 40x, but most stereo microscopes allow you to change magnification via a control knob on the body.
This is the maximum distance the objective can be from the subject and still focus. This is an important feature in a stereo microscope. Models with a short working distance may not accommodate very large subjects or leave enough room to work on the subject. 58mm (2.28") is typical, but some models such as the LOMO SF-50 have an enormous working distance of 170mm (6.7")
Monocular and Binocular Heads
Inexpensive models are equipped with a single eyepiece to keep price down, but at the cost of depth perception - a feature available only with two eyepiece microscope models. If you plan to work on a specimen as you observe, depth perception is essential. Observing with two eyes also reduces eye fatigue and improves visual acuity.
Illumination is not as critical on this type of microscope, since magnification is lower. However, all serious stereo microscopes offer some form of built in illumination, either from above the subject or below the subject, or both.
A stage plate is a glass or plastic platform the subject rests upon when you observe. Stage plates come in different colors, either black or white, to improve contrast between the subject and the background. Clear glass stage plates are also supplied on models that offer illumination from below the subject. Some industrial models or inexpensive models may not offer stage plates.