Grammatical rules are fundamental
Mike Rawl's system for remembering when to say "I" and when to say "me" is exactly what my Dad taught me years ago. It's a shame there weren't some demonstrations, however.
They taught all this in school. At least, they used to, when education was supported and funded. Yet, almost without fail, people reverse 'I' and 'me,' using each where the other belongs.
Dad was an advertising writer, and being correct was important to him. He asked: "Would you say 'Me went there?' Would you say 'Him went there?' If you answered no, then don't say 'Me and him went there.' Say 'He and I went there.' It's that simple. Try it.
"Would you say 'I bought a pizza for I?' No? Then don't say 'I bought a pizza for you and I.' Say 'I bought a pizza for you and me."
You'll still hear others getting it wrong. You'll hear it in song lyrics, on TV shows - all over. But, just in case you really have been wanting to get it right - this is the way to remember, even if you don't remember the rules they taught in school.
Now enjoy that pizza.