Your camera can be used to photo the virtual image in an eyepiece or in the trinocular port. You don't need to have a fancy camera, a point and shoot will do for basic work. That's how most pathologists did it in the beginning before cheaper clinical cameras were available.
The issue is, are you looking to photo slides (no significant depth of field in a tissue section 5 microns thick) or three dimensional sections? The type of microscope used will differ. The 3D specimens are best photographed with a long-working-distance objective. Regular diagnostic microscopy (transmitted light, specimen on glass slide) use short-working-distance objectives. Also, are you planning on illumination from below (transmission) or do you plan to use reflected light? What magnification? 2x to 10x - bellows are enough. Lighting systems are important. I am thinking about getting or making a fiber optic source for home macro on a stand.
I am a pathologist. Feel free to contact me. For standard thin-section (5 micron) transmitted-light microscopy, I have a dedicated small camera on the trinocular vertical port. Electronic shutter, controlled by computer program. The microscope and camera sensor/program are Olympus. Note that microscopy company programs do not have the same ADC and RAW processing as standard cameras - there are no "fudge factors" - the aim is to have more transparent quantitative response.
Nikon and Olympus have great reference sites about microscopy. "Microscopy U." Also, check out their yearly contests, especially Nikon's famous Small Worlds yearly photomicrograph contest, archived at their site.