All modern purpose built microscope cameras are excellent, I use an Olympus SC 100 10 MP colour camera on an olumpus BX 53 DIC research microscope to image live protists. An excellent camera after 3 years and 12,000 images no problems. Some images on my web site www.protozoa.com.au
If you can tell me your technical requirements, I can suggest something - but there is no "best" camera for all purposes. I myself use Nikon, and out of my experience, it is for me a better choice than Olympus. However, this is my subjective answer
1. I have used both Nikon and Olympus digital cameras to document plant tissue culture, protoplasts, and other experiments. I consider that both brands are high quality. They have simple and complex models. The advanced models have more functions. I, personally, especially pay more attention to a camera's capacity and power of 'close-up focus' and 'blow-up' functions in taking pictures, since we routinely take close-up pictures.
2. Nowadays, a lot of microscopes (even a simple dissection microscope) have already equipped with their own cameras. If you wish to buy a microscope and a camera separately, you might also need to purchase an 'adapter' to connect your own camera to the specific microscope eyepieces (see attachment for an example). This will also take you some time to figure out/choose, because the adapter should fit both your camera and the eye pieces of your microscope.