For proper Doom MP i would suggest Zandronum or Zdaemon (if you bought the originals in Steam you can use the wad files from there). Plenty of mods to keep you going, Brutaldoom getting the most attention these days.
As for the new Doom, single player has always been the "bread and butter", still looks good enough to give it a go later on. And yes, i played this from a floppy disk on a Windows 95 system back in the day, and renting it from the local videostore for the SNES occasionally. Good times.