Self-host a minecraft server with high security

You can take a look at mineOS, a small Linux distro that runs only a minecraft server. Put that on a dedicated machine or in a virtual one and set your router to forward the standard port (25565) so that machine's IP. Even if the (virtual) server is compromised it is virtually impossible to break out and cause harm to your remaining network - assuming your network is not setup without any password protection or authentication mechanism of course. If you want to be even more safe, set up a DMZ.

Alternatively, set up a LAN server that cannot be accessed from the internet and offer a VPN connection to those you want to allow access. This is less secure but probably easier to setup.

I highly doubt the Minecraft server is that secure, especially since it's Java from what I understand. That said:

1. Install a good firewall. I recommend Comodo for Windows.
2. Enable all the security features you can on the firewall, like Defense+ for Comodo. Note that some features may decrease network performance, which may be undesirable.
3. Block all ports except the ones used by the Minecraft server.
4. Set the Minecraft server to be the only executable allowed to access the internet (on those specific ports) or, if it's a .jar being run by Java, allow javaw.exe
5. You may want an antivirus, just in case; I currently run Microsoft Security Essentials, though I don't know that I would recommend it (its protective capabilities have not yet been tested on my machine).
6. For things like Windows settings, check out this MSDN article (pretty technical).

That should be enough to stop most hackers. Hackers prefer easy targets, so if you don't make someone angry they'll have no reason to target you :P