A Student Microscope
A microscope for a student should be rugged. Despite the best instruction and pleading, the microscope is going to be abused. It will be left uncovered. Things will be splashed on it. Cords will be tripped over. Durability will be its only protection.
Get a heavy one. When it is bumped into, it will stay put. If it has a cord, the cord just might come out of the socket instead of the microscope getting dragged onto the floor.
A student microscope should not be too expensive. It will not need high power oil immersion objective lenses. Most professional laboratory microscope work is done at 400x magnification or less, and a student microscope can put the value where it is needed.
That said, there are some corners you should not cut. A microscope without a sub-stage condenser is half a microscope. Many hours of fun can be had looking through that half, but that microscope cannot easily be upgraded as the student grows in ability and interest. If the microscope does not have a sub-stage condenser, the higher power objectives will not resolve enough detail to actually justify the magnification. What was blurry at low power will be bigger and just as blurry at higher power.
Whether the student microscope is monocular or binocular will depend on the budget, as this is a good place to save money. I will be showing you how to attach digital video cameras to the microscopes, so that the benefits of using both eyes can be had without fancy binocular eyepieces. But a cheap camera will not have enough pixels to give as good a view as binocular eyepieces, so unless you have a very nice camera, the binocular eyepieces will be nice if you can afford them.
A good student microscope with achromatic 4x, 10x, and 40x objectives, an Abbe condenser, and a monocular eyepiece is not cheap, but won't break the bank.
Wedmore SP14 Microscope $215
Celestron Advanced $330 http://www.microscopes.com/ms-ca-lm-loupe.html
Brunel SP100 Monocular semi plan objectives $416 http://www.brunelmicroscopessecure.co.uk/acatalog/microscopes-monocular.html
Celestron Professional $580 http://www.microscopes.com/ms-ci-mi-44108.html