I'm a bonafied cast iron gal. I use mine about every day. You've gotten a lot of good info, but as is the nature of things most everybody seems to have a different method.

I'll throw in my points... I SWEAR by LARD. Pork fat is the VERY VERY VERY best fat for seasoning a cast iron pan. Coconut oil second. Butter third. IME, anyway. Palm oil shortening might be good as well, but I've not tried it. I wouldn't even bother with other oils... Saturated fat is where it's at. Most vegetable oils get thick and gummy, not thin and slick. Who ever said to go on bacon frying spree had it right... That is the lazy man's seasoning practice there.

As far as frying and egg... Please do yourself a favor and DO NOT let your pan get TOO hot. Yes, WARM the pan then add the fat. But if your egg lets off more than a very weak sizzle when it hits the pan you are gonna have a tough rubber egg with the creepy crispy edges(maybe people like that?

) that is more likely to stick. Room temp eggs stick less than cold. And I don't know if you have ever seen the old school directions for how to fry an egg, but they would basically swim the egg in fat and spoon the hot oil over the top to set it. I flip, personally, but still like a good healthy layer or fat in my fan... My eggs float right onto my spatula... Tilt the pan towards your spatula. Scrambled is different... I pour the prescrambled eggs into a moderately hot and oiled pan, let it sit 15 seconds or so, slide/scrape the spatula over the bottom of the pan pushing the cooked portion into a pile of sorts, keeping it moving... this allows the runny stuff to spill into the pan. When most of the runny stuff is done, I flip the big pile of cooked to set the runny stuff on top. Turn off your heat(cast iron holds a lot) and chop up the big fluffy pile of scrambleds. This takes all of two, possibly three, minutes for a dozen eggs. It would be probably thirty seconds for two or three eggs. Don't have your heat too high and don't over cook your eggs... Your eggs will taste better and your pan won't get so gunked up.
When all is said and done, I don't even wash the pan... I just let the pan cool off a bit and wipe out the little crispies left in it. If the crispies are persistent I'll run warm water in there and gently(or firmly, no big deal really, it depends) scrub out with a stainless curly scrubby thing. Don't be afraid to leave your pan greasy! Water ought to bead up and roll off. I don't worry about rancid oil or anything... I use it so often, it doesn't sit around in there. If it has been a while I'll heat my pan and wipe out with a damp cloth to remove any residual oil that might be "off".
There is a delicate balance... Yes these things take a beating. You can really screw them up a thousand times and then fix them. The line begins where you get tired of fixing. It's a learning curve and you'll figure it out. It's fun, and a challenge. And I am PROUD of my pan, in a weird way.

It took a lot of scrubbing off screwed up gummy seasons, rubbing out the rust, smoky kitchen, cursed scrambled eggs to get my pan to it's silky black duck-like shine. And yes, I CAN make pancakes without adding fat to the pan. But it took my three years of fiddling around to get my season right. Good luck and don't give up!