Sorry but I'm slightly confused about EV's, and especially IV's and wondered if someone could clarify about them. I read up on them recently, but the IV's one didn't seem to make much sense. EV's seem different than what I originally thought, so let me spell it out.

EV's

What I thought: You fight a bunch of the same Pokemon to increase a certain stat, can't max out every stat for that Pokemon. If you breed such a Pokemon, the baby will have higher than average stats, and if you EV train that and breed it, same with the baby and so on. Long enough it's possible to have max stats on every stat of that Pokemon.

What I think now: Pretty much the same, minus everything with the breeding aspect of it. So if you want a strong Charizard, and raise it's stats and use all of the EV's, is that it? Nothing more can be done to make that Charizard stronger, or have another, stronger one?

IV's

WHat I thought: No clue

What I think now: Doing calculations on a stat to find out what number it is (0-31), and the higher that number, the more that stat will be able to be raised...I think? Is it really worth it though, since it's recommended not to do the calculations until level 50? Would suck only to find out the IV sucks after getting the Pokemon to 50.

Am I at all on the right track here? And is it at all possible to have a Pokemon be stronger than one EV training on it?