Where can I build a real website using html?

I want to start building my own website which can be accessed by anyone.

If I am correct, the Treehouse worksheets cannot be accessed outside of my own account. They are only practice worksheets and the website that I create with it is not "real". It is only a practice website. Is this right?

While it is useful to practice with the worksheets while viewing the video lessons I would like to start practicing on a real website. This first website that I make will be solely for myself for practice purposes. It will be about my dog. If it is good enough then I can add it to my portfolio, if not, then I will have something to be proud of which can be accessed from anywhere (and which I can show off to friends).

I am not familiar with the "website building" vernacular so my apologies if I sound roundabout in my question. What program/tool/"non treehouse worksheet" would you guys recommend I use? I believe that I would have to purchase a domain, correct? I want people to be able to search for my site so that if they do a google search, for example, "entlebucher mountain dog yogi madison wi" then my web site would show up in the search engine results.

By purchasing a domain I can name my website whatever I want assuming the name is not already taken, correct? It would be cool to call it "yogithebestentlebucherdog.com". If purchasing a domain is expensive then how do I go about making a website otherwise?

Basically, I don't want to put all this effort in practicing by building a website on the treehouse worksheets if I can't actually view it as a real website.

Thank you from Natalia in Madison, WI!