> "Stick with the 13 web safe fonts" assumes that operating systems won't change. There used to be 3 web safe fonts. Use whatever typography you want, so long as you self host the woff files.
Indeed. 10 years ago, “font-family: Georgia, Serif” was guaranteed to work and look the same on pretty much all computers out there. Windows had all of the “web core” fonts (Georgia, Verdana, Trebuchet, Arial, even Comic Sans). Macintosh computers had all of the “web core” fonts. Even most Linux computers had them because it was legal to mirror, download, and install the files Microsoft distributed to make the fonts widely available.
In the last decade, Android has become a big player, and the above font stack with Georgia will look more like Bitstream Vera than it looks like Georgia on Android.
The only way to have a website have the same typography across computers and phones here in the soon-to-be 2020s is to supply the .woff files. Locally (because Google Webfonts might be offline some day). Either via base 64 in CSS or via multiple files; I prefer base 64 in CSS because sites are more responsive loading a single big text file than 4 or 5 webfont files. Not .woff2: Internet Explorer never got .woff2 support, and we can’t do try-woff2-then-woff CSS if using inline base64.
Even with very aggressive subsetting, and using the Zopfli TTF-to-WOFF converter to make the woff files as small as possible, this requires a single 116 kilobyte file to be loaded with my pages. But, it allows my entire website to look the same everywhere, and it allows my content to be viewed using 100% open source fonts.
Then again, for CJK (Asian scripts), webfonts become a good deal bigger; it takes about 10 megabytes for a good Chinese font. In that case, I don’t think it’s practical to include a .woff file; better to accept some variance in how the font will look from system to system.
Edit In terms of having a 10-year website, my website has been online for over 22 years. The trick is to treat webpages as <header with pointers to CSS><main content with reasonably simple HTML><footer closing all of the tags opened in the header> and to use scripts which convert text in to the fairly simple HTML my website uses for body content (the scripts can change, as long as the resulting HTML is reasonably constant). CSS makes it easy for me to tweak the look and fonts without having to change the HTML of every single page on my site, but as the site gets older, I am slowing decreasing how much I change how it looks.