I think XBox 360 has the Classic Doom Collection available on their online store. It's a digital download release only, no physical copy to buy that I'm aware of. True there's the BFG Edition but for some reason, I don't dig playing that version of Doom 3 or the classics that come on the disc. Plays a little off to me for some reason. I only play that digital version every so often though as I'm not crazy about using a controller for Doom, it seems to slow to me if that makes sense. Mouse/keyboard setup is so much faster & precise for me.
As for multiplayer these days, I think the classics on the BFG Edition might have a Death Match option that goes online & the digital Classic does too I believe. No idea how to get multiplayer PC. Never got into doing online multiplayer at all for any game or system. Don't see the appeal in death match's or capture the flag type games. Co-op story mode games I'd be down for but that's a rare one to find these days.