Note for the Zandronum servers:
If we decided to go forward with this I will set up a video tutorial for installing and configuring Zandronum, as well as a list of some different mods we could do. There's a maaaaaasive amount of mods out there that can drastically change the gameplay, so we have lots of variety to pick from.
Zandronum itself is free and runs on most PCs as long as they're no older than 10 years old, and it runs on Windows, Mac, and Linux. Doom and Doom II (often Doom II is more commonly used for online play with mods) are not free but can be gotten from Steam for $5 each or from GOG for $10 for the two.
You can also try your luck searching around.