You should start with the nature of time. Once you understand that, you'll understand that there's no actual time flowing inside a clock. Then you'll understand that when a clockwork clock goes slower, it's because the clockwork is going slower. Then when you apply that to an optical clock, you understand that an optical clock goes slower when it’s lower because light goes slower at the lower elevation. Because the speed of light is spatially variable. That's what Einstein said: “the curvature of light rays occurs only in spaces where the speed of light is spatially variable”.
Once you know that, you know why light curves in a gravitational field, then when you apply the wave nature of matter you can understand how gravity works. And so on. You understand one thing, then you can understand the next, and the next, including things like electromagnetism. And when you do understand them, they're all much simpler than you thought. But IMHO if you don't start with time you just can't get a handle on anything.