I'd suggest starting an Apple II emulator, grabbing one of the fine books on 6502 and Apple II programming available on PDF and learn what happens after your C compiler translates your code into what the lower levels of your computer actually run.

You could also play with a TRS-80 or MSX emulator, but I find the Z-80 a bit too complicated. If you are going to the lowest levels, the simpler, the better.

C has its value, but knowing how the bare metal behaves is useful too.