What is the correct way to install modified versions of standard packaged applications?

I want to make some small trivial UI changes to various standard applications such as evince, kate, texstudio, etc. Since these are all open source applications, I know I can just download the code, make the change I want (possibly easier said than done, but that's a separate discussion), compile, and run the resulting binary executable. **Question:** How to properly install the modified binaries on my system? I know I could just keep them somewhere in my home folder and modify $PATH in my .bashrc appropriately so that invoking them in the terminal leads to my modified version rather than the standard version. But I'd rather put my modified binaries in the usual location /usr/bin or whatever (overwriting the standard version currently sitting there), so that my entire system (launcher menu, browser, etc.) uses them. How should I go about doing this so as not to break anything? Should I just copy it to the right location using cp, or should I try to create a .deb package with my modified application and then run sudo apt install on it? Will the source code typically come with a Makefile which generates said .deb file for me? What happens when sudo apt upgrade downloads an updated version of one of these applications? Do I just recompile my version and overwrite it again? I realize the answer may depend on what application I'm modifying, but I hope there may still be something helpful one can say in general. If not, I'd be happy with an answer regarding any of the specific applications I've mentioned above (evince, kate, or texstudio).