P2P network? It sounds like you're making this much more complicated than it needs to be. The people saying Mint isn't good for networking are probably referring to using Mint as a network/DHCP server, that's not what you need.
You have a router, you already have your own subnet, so just give the machines a static IP. I'm not familiar enough with Mint to give you step by step instructions, but you typically just edit /etc/network/interfaces and change
Code:
auto eth0
iface eth0 inet dhcp
to
Code:
auto eth0
iface eth0 inet static
address 192.168.1.2
netmask 255.255.255.0
gateway 192.168.1.1
Changing address, netmask, and gateway to suit your specific subnet.
Or there's probably a GUI config as well, maybe right click on the network indicator in the panel or go to the system config menu? All you need to do is switch from DHCP to static and fill in your address, netmask, and gateway. You may need to enter a DNS server address as well, you can get that from your current config, or your router's config page, or you can usually set your router's IP and it'll forward to the necessary server, or you can just enter 8.8.8.8 to use Google's.
Any Linux distro can do this without issue.
