Different light microscopes serve different purposes. This article gives you an overview.
These are sold in toy shops and other places which are not specialized in microscopes. They can be easily identified, because they come with many accessories, such as slides, prepared specimens, plastic pipettes, tweezers etc. and because some of them are advertised with ridiculously high magnification (750x and more). There is general agreement in the microscopy community that these microscopes should be avoided, as their price to performance ratio is not satisfactory. These microscopes do not have objectives manufactured according to the 160mm (DIN) standard. Resolution is low, focusing is difficult (plastic parts), the field of view and eye relief are low, brightness is low. Many people buy these microscopes anyway, because they simply do not know where else to buy microscopes.
Educational and student microscopes
These are small, portable devices. They generally have a 10x eyepiece and three brightfield achromatic objectives (4x, 10x and 40x). The lamp is often halogen or LED, some are even battery operated so that it possible to use them in a classroom without a power supply. Many amateur microscopists use these and are quite satisfied. You should not confuse educational and student microscopes with toy microscopes that are sold using these descriptions. Educational and student microscopes use standardized DIN objectives and have a body made of metal. Some even have a condenser with a diaphragm to control resolution, contrast and depth of field.
Routine and laboratory microscopes
They are a bit larger and heavier than student microscopes. The transition between student microscope and laboratory microscope is somewhat unclear, as often the same microscope body is used with different components attached. These microscopes have a condenser, often Köhler illumination, a mechanical stage, focus lock, and a revolving nosepiece which can accept not three but maybe four or even five objectives. The larger base allows for a stronger lamp. Many routine microscopes are equipped with a binocular head to make long-term observation easier.
They are quite large, not portable, expensive, and quite modular. Some have many different objectives and filters attached which can be easily exchanged. Often different research groups share the same microscope and the device must therefore be quickly adaptable.