Maybe that's how it will turn out in America, but it's not a given. I saw a breakdown of how the post-neutrality system works currently somewhere else, maybe it was Portugal.
It's not the user who pays more for speed, except in the sense that you do that already today by buying a faster connection. It's the website operators who pay for speed. What you pay more for is range of content. A bit like selecting a set of channels with a cable company, except there were more options to choose from. If you want access to everything you pay a premium price, or you can get a more limited package. Social media and video download were two options I remember seeing there.
Also, maybe not every carrier will carry Netflix for example. Depends how much Netflix is willing to pay them to carry their stuff, like with TV channels today. Maybe some carriers will offer porn and others won't. Etc.
And which carriers you even have access to will depend on where you live, just like today.
All that depends on what regulations and limitations are put in place, and I have no idea how that will be managed here. Maybe carriers here will be forced to carry all content. The devil is in the details.