If you want your website to be a full-time business and turned into a company, what would you register it as? LLC? Ltd? Inc? And how do you register it as one of those?
I'm starting a limited company at some point this year. But with regard to how you do it, it is going to vary by country. You should check the governmental website of which country you intend to start the company for accurate information.
I started an LLC on new years. It was easy, and cost effective. It was only $180 in my state, but other states it can run $700 or more per year. It doesn't just vary based on your country, it also varies depending on what state in the US you're in, as well. If you're in the US, something like LegalZoom can set it up for you, or you can contact the state and do the paperwork yourself. It's not difficult.