Hosting chronology something like: home Linux box on ADSL, 2 different shared hosters, 1U in a colo facility, back to earlier shared hoster.
For my real-name vanity domain, I went with a `.org`, since I didn't want to be a `.com` in personal life, though today I'd prefer `.net`. (The longer story behind this is that, early in dotcoms, I very quickly got tired of being at social parties of grad students, with MBA students always wanting to talk to me for startup reasons. Also, CS departments and culture were changing due to the gold rush. Going "non-profit" was an idealistic youth reaction.)
The reasons I keep the vanity domain and hosting include:
(1) I'm not signing over rights to some snooping companies to snoop on my email, nor will I implicitly endorse that practice. (IMHO, the current practice of corporate snooping on everyone's private communications is a bad for society. All this time, we techies have been shirking our responsibility to advise people about what they're signing away, and why that's an undesirable direction. I haven't done my part, but I'll try not to make it worse.)
(2) The vanity domain name gives me flexibility for where&how I host, and doesn't lock me into anyone. (Though I'll remain loyal to a hoster who's worked well, even if that means my site is not a showcase for a currently popular service. I've done novel things on AWS professionally, and I shouldn't have to prove anything with my quaint little personal site.)
(3) I've run the canonical Web pages for various niche open source projects, and there's never been an obviously good third-party permanent home for them. (I did almost move those projects to a `git`-centric third-party service, fairly recently, but then my first choice service was acquired by a very different corporate culture, and this also raised the question of how my second choice is going to change (due to competition, or presumably being courted for acquisition). Moving is a lot of trouble to go to, for a situation that might make me want to move again soon after that, so I stick with my ancient site design and hoster.)
I have mixed feelings about the Web site's dated visual design, and I think this is a consideration for anyone who makes a Web presence that will last for years... Mine has looked almost identical for ages, and now feels personally "genuine" to me, compared to better but generic modern looks. While the look stayed the same, the implementation has moved from `table`, to CSS that mimiced the `table` look, to CSS that's responsive while still respecting user's preferred font size. In parallel, there was also a move from HTML4-ish, to XHTML, to HTML5. Along the way, I dropped some unnecessary features that were flashy when I did them, like code syntax coloring (for which I rigged up Emacs into site generation).
I suppose a dated-looking site filters out job opportunities from people who insist that one's personal Web site showcase their best frontend practices. It could stand another look, at tweaks or makeover or complete rethinking, but I'd rather invest unpaid time in contributing to an open source project or techie community, than futzing around with the vanity domain.
You might keep updating your own site, but at some point you might have better things to do, so try to leave it in a style you won't mind being frozen at for years.