The easiest way to do this is to get a second router, assign it an unused public IP address, and forward the appropriate ports to your server. The server would be physically separated from the rest of your network. As an example, lets say you have a cable modem with a built in 4 port switch and a block of 5 usable IPs 188.8.131.52 through 184.108.40.206. You'd plug the WAN ports of the two routers into the cable modem, assign 220.127.116.11 to one router and 18.104.22.168 to the other. To access the server, you'd either have to physically be in front of it, use a program like TeamViewer, or forward port 3389 to the server so you can use RDP.
A more sophisticated way of doing it would to get a router supports 1 to 1 NAT. That would allow you assign one public IP address to your server and another for the rest of your network using only one router. Depending on the router, you could either create a separate sub-interface for your server to keep it separate or use VLANs.
If you don't have much experience, I'd probably go with option A unless you have a need for computers on your network to be able to access that server locally.