The Internet is not free speech. It's not the 1990s anymore. It is not a series of cute websites about people's cats or art projects. It is now a massive utility that coordinates communication and commerce. Corporate, educational and government websites are hosted on it. Commercial speech is ubiquitous online, which legally is not a class of protected speech. The Internet is the public square, the telephone, the government office, the bank, the grocery store, and the department store, and dozens of other things, all at once. All of those things are regulated to some degree. The idea that an amalgam of all of them should not be regulated is one of the most absurd ideas I've ever seen taken remotely seriously.
It's crucial to note that "the Internet" is not akin to the airwaves. There's both private and public infrastructure, research and mechanisms at play. The airwaves do get used, and at that point there is a public regulation of a finite resource, but there are also theoretically non-finite resources like fiber-optic infrastructure. Therefore, the Internet should be lightly regulated. There should be no regulations like on television. (I also believe that obscenity, including simulated child pornography, should be allowed with virtually no restriction, but the Courts disagree, and so under the present Constitutional interpretation, it would also be subject to regulation).
And, of course, "the Internet" is a cross-national phenomenon, so no one country should behave with unlimited power and disrespect for other countries' laws. Still, utter legal fictions, like a server bank nominally operating off shore even though the actual business is all being done in a specific country, should not be tolerated.
Even with a much lower standard than was practiced on radio or television, Internet regulation would include
*Reasonable efforts to deal with fraud, malfeasance and financial crimes online
*Reasonable policing of outright harassment, intimidation, and other behavior
*Aggressive policing of tax evasion, human trafficking, and black market interactions
*Consumer complaints and regulation for online retailers, businesses and services
*Efforts against online prostitution (again, yes, prostitution should likely be regulated but legal, but that is a separate question)
*Controls on child pornography (again, child pornography with no actual child victims should be allowed, but actual depictions of sex acts with a minor or of nude or sexually exploited children should be aggressively investigated and prosecuted)
*Regulations against anticompetitive behavior
*Enforcement of appropriate wages and employee-employer relationships online
*Regulation of contracts
*Regulation of banking
*Regulations against shell companies and illegal corporate maneuvering
This is far from an exhaustive list: other categories would see regulation. Whether that regulation would involve criminal investigation, less aggressive policing, the opportunity for torts, and/or whatever else should be determined in each case, but laws should be constructed for all of these areas.