Otherwise, everything applicable from back then still is today. Any time anyone mentions PHP on forums like this, there's always fashion-conscious people who jump in to attack it. But I'm still building brand new websites based on it, and people still express their gratitude, never once saying there's any problem because the site uses PHP.
MySQL is still going strong, and there's some alternatives that are compatible, like Percona and Maria.
What I'm getting at is, I don't know why you need to update anything. If you're trying to get a specific job, then you need to use what they do. But for just building things in your free time that work on modern web browsers, you already know what you need to know. You could probably even run the same exact version of server and authoring tools you did before, and it should display fine in the latest web browsers.
It's different if you want to build something like a mobile app, or Windows software, because those platforms changed significantly since the '90s. There's languages now that didn't exist then, and new tools you've never seen before.
But on the web, any text editor, HTML, and any language you want for the backend is fine. Just like I still write .sh scripts, and they get the job done.
It's more important to spend that time on family, and your career. Since the stuff you already know still works, there's not much need to use anything else. Unless you're worried about what the kids think, and how they'll judge you.
"What I'm getting at is, I don't know why you need to update anything"
Shocking advice. There is a huge amount to learn. Any developer coming from the 1990s needs to re-learn all their technologies or they are going to have a very stressful time delivering anything appealing to users expectations in 2016.
"Since the stuff you already know still works, there's not much need to use anything else"
This kind of mentality leads to becoming deadwood and unemployment. Developers must keep learning especially with the rate of change of technology over the past 5 or so years.
I'm building things the same way as I did at around 2000, and my creations are just as relevant today. Most of the fancy JS stuff we could do in the '90s. The new stuff is not about basic websites, but how some new additions of HTML5 work. Most websites do not need those though, and if they do, then you learn those specific things.