The most important thing for you to know is the rule that Internet providers are required to pass only legal content.
While it's unlikely that anyone would seriously suggest that it's okay for an ISP to be distributing child pornography, the real issues go beyond that. Legal content also includes blocking material that is protected by copyright, or is otherwise prohibited from sharing. And here lies the problem.
Who determines what legal content is? Can an ISP decide that the ad in your cosmetics or clothing catalog includes a person who appears to be under 18, and therefore might not be legal to transmit unless the ISP sees a parental permission slip? Can an ISP inspect your company's traffic to determine if it contains only legal content? Can the government shut down Amazon because it distributes books for free that are out of copyright, on the theory that the books might be still under copyright somewhere?
And those are only a few of the problems.
While the FCC gives examples of what it considers illegal content, it provides no guidance for who determines the legality of content. Effectively, given the commission's public complaint process, companies could find themselves effectively shut off from the Internet by gripes from disgruntled employees or customers claiming that material on the company website is illegal. Insiders could claim that the material that the company stores in its cloud-based backup site contains illegal material.
Of course the FCC will investigate, but what happens in the meantime? Does everyone on the Internet see your address as one that they should block? At this point, nobody knows. Worse, nobody is likely to know for some time as the new rules make their way to the Federal Register where they will become active. While lawsuits seeking to overturn this rule are certain, and while congressional action is possible (but unlikely), the bottom line is that nobody really knows.
Right now, the best thing you can do is to make sure you're very careful with the material you publish online-make sure you have the rights to the material, for example. Have whatever forms available that demonstrate that whatever images you publish are legal. And make sure you encrypt everything so that an overzealous ISP out there can't decide that your e-mail is somehow illegal.