Are apple.com's Compatibility lists for mice and keyboards comprehensive?

My iMac (21.5-inch, late 2013) does not appear in the Compatibility list for any Apple mouse or keyboard for sale on the apple.com website. If that really is true, are there options? Do I really have to find an old mouse and keyboard somewhere, that still work? Mine don't. Some people claim to be using mice/keyboards with computers that aren't on the list, but how do I know if that's going to be true for me? I don't want to waste time and money ordering something that won't work. Hard to accept that my well-running machine can't be used because the new mice and keyboards aren't compatible.