For normal brightfield microscopy industrial cameras are very good (the internal sensor chipset is the important component, and there are only a few manufacturers globally) and usually offer both USB UVC and HDMI output. Monocular optics are very cheap and offer free-zoom (so-called 'zoomtube', great for video) and configurable magnification.
In terms of reflected light microscopy, you are going to get very good results with off the shelf ~$100 systems (camera+monocular zoomtube) and LED ring lighting (preferably anti-glare with configurable polarized filters).
You get a solid upgrade switching to transmitted light microscopy. This requires some sort of transparent stage with underside lighting. This can be as simple as placing an unprepared sample on a slide and shining any light (like a phone LED) through it. But it works better if the light is even, the light is collimated, the light is focused, the light is controllable (ie. light source + collimator lens + condenser, at precise relative distances).
At high magnifications the focal plane is very thin. You will need focus stacking for many unprocessed specimens, which can be achieved in software but requires a rigid platform and a steady hand.
Around this level you get some good upgrades from taking thin sections with a razorblade. You can buy mini microtomes but they're basically razorblades. Just buy razorblades. Staining also helps, read for example http://digitalcommons.mtu.edu/cgi/viewcontent.cgi?article=11...
If you are serious about your images, you can buy a cheap calibration tool for measurement purposes and synchronize it to software for markup and addition of digital scale purposes.
Beyond these you certainly need a rigid platform. To this point things are quite cheap, depending upon your requirements you could be only $200 in and happy with a range of stains, thin sections, configurable lighting, aperture, precision movable stage, etc.
Once you're in this territory you probably want a better turret and oil objectives. This is expensive.
Motorized stages, focus, filters/polarization, etc. are all options, often hard to retrofit to existing scopes, but of great utility depending upon what you're looking to achieve. I am sort of designing around this area. I am interested in structured light microscopy, which has recently been achieved for 10K EUR by academics in Europe. I may offer something cheaper if I can get it working.
Beyond that the next steps are precision methods like darkfield, phase contrast, DIC, fluorescence, etc. These get expensive quickly, requiring additional matched hardware and dedicated objectives. I know little about these techniques yet.