I've personally written a decent portion of this:https://en.bitcoin.it/wiki/Introduction
I also took care to take out more technical things that aren't relevant on an introduction.
To respond to some of your points:
"And the larger the string gets, the harder it becomes to verify."
No, the strings used in transactions will always be the same size. They will always be just as easy to verify. Everyone verifies them, not just miners. Miners do an additional task beyond most people: they create blocks. Creating blocks is very difficult.