For me, the key is understanding the temperatures at which the white and yolk solidify (about 140 and 165*F, respectively), and the protein structure during each cooking phase. When you can see the changes happen and know (physically and chemically) what is going on without thinking about it, it takes a lot of the 'mystery' out of egg cookery.
Also, working breakfast/brunch in upscale restaurants will make your egg game strong as fuck if you ever have to opportunity. At first it's frustrating because there will be a lot of recooks, but once you find the groove, shit is all gravy.
Salt and vinegar change the coagulation points of egg proteins significantly as well.