There are two scenarios with different solutions:

• You have different pictures and want to keep the color and brightness comparable from picture to picture. (Automatic exposure and automatic white balance can negate the differences you're trying to capture.)
• You have subtle variations in colors/shades in the same picture and want to be able to tell them apart.

Consistency over multiple pictures

You need the same lighting, exposure and color balance.

Two common solutions are:

• Use a camera where exposure and white balance (WB) can be set manually, and keep everything the same between shots, including light sources and distance between light source and subject.
• Include a gray card in the picture as an exposure and WB reference, and use the WB adjustment frequently found in image editors. RAW is best for this (rather than JPG), as RAW has more leeway for adjustments afterwards. You'll need a camera with RAW support, which excludes camera phones and consumer webcams, but includes DSLRs, mirrorless and some compacts.
  (For scientific cameras I've no idea, but since they are explicitly scientific I can only assume that they give access to the raw data in one form or another, although you may need custom software to manipulate those data.)

Note that fluorescent lighting and sodium-vapor lamps are tricky, and can make accurate colors impossible. Avoid them if you can.

Incandescent light, photographic flashes/strobes and normal daylight are good light sources for accurate color reproduction - you want a light source that emits full-spectrum light.

Subtle variations in the same picture

I think this is primarily a matter of "bit depth".

More bits means that the sensor (or technically the ADC, the Analog-Digital Converter) can capture more nuances. One extra bit translates to twice the number of brightness levels. For an RGB sensor it's one extra bit per color and 2^3=8 times the number of distinct colors.

For reference, DSLRs and large-sensor mirrorless are typically 12-14 bits. Many/most of them can be connected to a computer, look for tethering options.
The USB cameras in your link are up to 10 bits, which may or may not be sufficient.

But: JPG and most standard monitors are limited to 8 bits, and some low-end monitors are only 6 bits. So to make the larger bit depth visible on a standard monitor, you'll need to shoot in RAW and find a mapping from a many-bits color space to a few-bits color space that retains the distinctions you want to keep.

By converting to a smaller-bit-depth color space you are inevitably discarding information. But when you define the mapping yourself, rather than leaving it to the default JPG conversion, you can decide which color and brightness distinctions to keep.

I don't know what kind of support the USB cameras offer for such remapping, but I think that's what you are looking for.
And you might be interested in a high-bit-depth monitor to go with the camera, certain high-end monitors can display 10 to 12 bits of color.