cbtsam wrote:
...I've read that I should do my work in Photoshop using the Prophoto color space, rather than Adobe RGB, since its just about the biggest color space...
Yes. ProPhoto is currently the widest color space commonly available and working in it with 16 bit files such as TIFFs and PSDs will give the best quality edits. Adobe RGB is pretty close, if preferred or not able to use ProPhoto for some reason.
cbtsam wrote:
...Then I learned that I should downsize my color space to sRGB for most internet applications, even though sRGB is even smaller than Adobe RGB...
Yes. This is best because sRGB is much more widely used than Adobe RGB. Once you upload an image to the Internet, you no longer control how and with what it will be viewed. Many browsers and other software do not properly interpolate Adobe RGB, so it's best to convert to sRGB. Also be sure to reduce from 16 bit to 8 bit. Doing these things
after all your image editing and sizing has been done usually shows very little loss of image quality. It also results in smaller, more manageable files that display quickly and smoothly with a wide variety of devices and software.
cbtsam wrote:
...Now I've been told that printers' output uses an even smaller colorspace than sRGB, which rather surprised me...
No. This is not the case. You usually should use sRGB color space. I know some printers can handle Adobe RGB and even 16 bit files, but there's almost always no gain in image quality. it just makes for slower printing and may even waste ink. Many printing services and most photo-quality inkjets specify sRGB 8-bit files (usually JPEGs).
One difference between printing and online display is the pixels per inch you should use. For online display I usually set 100 ppi. For printing I usually use 300 ppi, which results in a larger file. These aren't hard and fast numbers.... some monitors display 96 ppi, while others such as 4K may show as much as 130 ppi. It's the same with printing... the larger the print and the farther away it will be viewed, the lower the ppi can be. 300 ppi is more than enough for even modest sized, closely viewed prints. 240 ppi is even usable. But if making a larger print where viewers will need to step back to see it, you might use 170 ppi or even less. An extreme example, a bill board that's viewed from dozens of feet away might only be 40 ppi!
I'm not aware of ANY "even smaller color space" that's being used for photo printing purposes. I wouldn't even know how to find or specify one in my software!
There IS a "CMYK" color space that's used for commercial printing purposes. For example, CMYK is used with offset printing where there will be separate plates made for each of the color channels and black (C=cyan, M=magenta, Y=yellow, K="key" or black). Perhaps this is what you've heard about. It is NOT "smaller" than sRGB and is NOT something that's commonly used by photo printing services or appropriate for printing yourself with a photo-quality inkjet.
There are a few other specialized color spaces, which I don't know anything about.
I like to keep it simple:
1. Camera set to Adobe RGB, though it really doesn't matter when shooting RAW.
2. Work on 16 bit images in Photoshop either in ProPhoto or Adobe RAW color space.
3. Size images to 100 pixels per inch for online purpose, 300 ppi for printing (unless otherwise specified).
4. After all the work is done, reduce images to 8-bit, sRGB for either online or printing purposes (unless otherwise specified).