What caches can be cleared, when wanting to keep settings? I do not know enough about the original purpose of the different caches. If I do a cleanup in a few months and clear many app cache items, is it safe for me to assume that most programs will not lose settings, if I clear the "cache" cache and leave the data cache alone?

Most programs means if a few lose settings, it is not a problem. There are many settings in many programs that took me quite some time to setup (and test).

By settings, I am referring to the applications own settings, not web settings, or settings that the application has access to. Take a game, for example. I do not care if the game is reset, levels are lost, or log-in is gone. But the settings for that game app must stay.  In a program, I do not care if it loses its thumbnails, and add-in parts, just that the settings for the program stay the same.

If this is all wrong, and programs are not normally supposed to use the data cache for settings, then tell me about it. I just assumed after losing some carefully selected settings that it is there in the data cache.
Any cache can be cleared. Clearing the cache will not remove app settings. 

Read more from this closed question in StackOverflow (should be migrated here):
What's the difference between clear cache &amp; clear data in android settings