A domain name registration is essentially the only form of digital identity that you actually own specific rights to—you are sharecropping everywhere else, meaning that your identity (your gmail/google account, or facebook profile, or whatever) can be deleted without your say. I believe it is an *essential* part of one's identity in the modern age.
My preferred domain registrar is [porkbun.com](https://porkbun.com). Weird name, great service.
While there are countless fun domain extensions available these days, sticking with the .com/.net/.org can offer you a slight bit more security, as they are regulated by ICANN, whereas nearly all of the others are maintained by specific companies or countries (which offer varying levels of ownership rights). But really, anything will probably do just fine.
The cool thing with owning your own domain name is that you now have a permanent home on the web, accessible to everyone (no matter whether they have an account on your preferred social network).
There are countless things you can do with it, even if you don't host an actual website there, from filtering email to redirecting to other webpages, or even "proving" your identity on some social media networks. Of course, there's *far more* you can do if you actually host a website(s) there!