getting into my home server from the Internet, with security

I am very new to this and I don't even know the terminology to use, so here goes:
I'd like to make an NAS box in my home serve as a box I and friends can log into from the Internet. Not to store files, but to hit web pages I'd like to set up.
The NAS box came with some software to do this --but-- it lets anyone outside get into any of my computers inside! I do NOT want that. I want the NAS to do everything and be a strong firewall for my little internal network.
I'm on cable 'net so it's the actual box to the outside world. Unfortunately, I do not have a static IP on the cable modem.
Between that cable modem and my little home network is a router that also has wifi and it serves ethernet to the house and wifi to the phone and tablet. From that router, one line goes into the NAS and all others go to stuff in the house. The NAS box has two ethernet ports but I'm only using one. It seems that the NAS is running a bastardized version of LIinux but I can't be sure. It's a Lenovo PX12-400.

So, how do I do this, please?

Thanks for help if you can.