For a serious compound microscope, look for a model with both coarse and fine focus, built-in illumination, light control via an iris and condensor and a mechanical stage. If you need to keep the budget down and/or don't have access to power, a model with a mirror is acceptable, but insist on a model with a fine focus control. It is very difficult to use high powers on a microscope
without a fine focus.
Try the excellent LOMO
MULTISCOPE BMH4-BF binocular microscope
(best buy). These are the types of microscopes
found in the typical college science or research lab and are the most used type of microscope
in microbiology and medicine. They require you to use and prepare slides.