Cameras for scanning and those for normal photographic purposes have very different requirements, though there is some overlap. Even a relatively affordable, 'old' camera can get you very good scanning results. All the cameras we have recommended here do, under the right conditions, be good enough to draw most of the quality out of a normal 35mm frame. You will often find a bigger increase in quality by upgrading other parts of your scanning system - therefore we recommend that you use the camera you have.
Mirrorless is preferred over a DSLR
Must have manual exposure settings
Must have interchangeable lenses (system camera)
Minimum resolution: 8MP for 35mm, 16MP for medium format
Full Frame sensors, for scanning, after seldom worth the extra cost over
A mirrorless camera with an electronic shutter/electronic front curtain will produce higher quality scans
Is a Full-Frame sensor better than smaller sensors?
For scanning - no. In our testing and from the testing we have seen in the community there is no big benefit that full frame gives you over APS-C, and probably only a small benefit over MFT (M4/3) sensors. If you have a camera with a smaller sensor you will probably see a larger increase in quality by upgrading your lens or light source, rather than to a full-frame camera. We know, in fact, that some lenses will give you better results on smaller sensors because the quality in the corners of the image on full-frame is significantly worse.
How much resolution do I need?
The digital resolution of your camera is important when scanning larger pieces of film, such as medium format, but less important when you scan 35mm film. For 35mm film we recommend minimum 8MP and for medium format, 16MP - these resolutions will not pull out every last bit of grainy detail in your film - for that, you want closer to 20MP and 50MP, respectively - but it will give you a pleasing image with most of the detail perserved.
Do I have to find a lens that works for my camera?
Yes and no - you need one that fits the lens mount. Luckily there are adapters between most of the systems, particularly for mirrorless cameras like many of the cameras mentioned here. You can read more about adapting lenses in this brilliant article.