^^I crack the eggs on the countertop, and more often than not leave some egg goo on the counter, or dripping on the way over to the pan on the stove, which means a messy cleanup. And a cleanup I can’t do right then because the stove is hot.^^

You are cracking them too much before carrying them over to the pan.

If the egg is standing upright, the middle of the egg, where it might wear a belt, is the weak point. That is where you crack it. Hit the table top so it side lands squarely against the surface.

Give one sharp tap rather than several gentle taps which shatter it into pieces - you want one larger split. That said, don’t overdo it, either.

Carry it over the pan with this one crack - the egg will be cracked but not "opened" and you dig the fingers in a little to open it at the crack but only when over the pan (or cup etc).

Use your thumbs to press inward and separate the shell, then pour the yolk and white from the shell into a bowl.

Don't crack the egg on the rim of a bowl as this creates small pieces of shell falling into the bowl.