So, what do I do with it now?
Stick with High Sierra. Its not going to be a problem for a while yet (heck, I'm still on Sierra) and I'm not even contemplating Mojave until the first update or two are out.
As others have said, HS is going to get security updates until 2020. Even after that, if its sitting behind a home firewall and you're sensible about web and email, the risk is small (and Chrome/Firefox might still get updates after that).
If you want to get a new Mojave-capable Mac as your main machine, maybe use the Mini as a home server for files/time machine/iTunes... Even less downside security-wise since you're not going to be browsing the web or opening email on it.
Pretty much any server software that you might run in Linux is available on MacOS via Homebrew/MacPorts if not as a "proper" Mac package.
Alternatively, If you do anything serious with your computer then its always good to have a spare.
...and by 2020, either Apple will have improved its range of affordable desktop computers to offer you something tempting - or it will be pretty clear that its never going to happen.
(One of these days, I'm going to need to run an ancient bit of PPC software - probably about 2 weeks after I decide to turn out the cupboards and throw away my 2004 Mac Mini...)