It's about effort and you might be better off with some hosting service.
But if you really want you would need
1) a router (like AirPort Extreme)
2) a fixed IP adress or a service like DynDNS to reach your router from outside
3) a firewall at least, better VPN setup, best even both
With this you can reach any NAS in your internal net you want to buy. I have a QNAP but other work the same way.
The big challenge will be the security of your network and files. People out there love to try to scan the net and find open ports.
That's why: hosting not an option ?