I had a little too much time on my hands and started wondering if I could write a self-modifying program. To that end, I wrote a \"Hello World\" in C, then used a hex editor
Self-modifying code is used for modifications in memory, not in file (like run-time unpackers as UPX do). Also, the file representation of a program is more difficult to operate because of relative virtual addresses, possible relocations and modifications to the headers needed for most updates (eg. by changing the Hello world!
to longer Hello World
you'll need to extend the data segment in file).
I'll suggest that you first learn to do it in memory. For file updates the simplest and more generic approach would be running a copy of the program so that it would modify the original.
EDIT: And don't forget about the main reasons the self-modifying code is used:
1) Obfuscation, so that the code that is actually executed isn't the code you'll see with simple statical analysis of the file.
2) Performance, something like JIT.
None of them benefits from modifying the executable.