If you insist on using your CD rather than using a GOG or Steam copy, you'll want to be able to get at a "doom.wad" file. Depending on the CD you have, it'll either be available as a regular file, or compressed as an LHA archive. In the latter case, you'll find either one file such as "RESOURCE.1" which you can extract directly with lhasa, or several files like "DOOM_SE.1", "DOOM_SE.2", etc, in which you'll want to cat them all together into a new "DOOM_SE.lha" file and then extract that.
For Quake 2, the most commonly used clients are R1Q2 and Q2PRO. I recommend starting with R1Q2 because it keeps the same look and feel of the original game but offers major behind-the-scenes improvements. You can get texture packs to make the game look more modern, but I don't like to use them.
A list of all active multiplayer servers can be found at http://q2servers.com/. You can usually find people playing action, ctf, deathmatch, and jump mods.
I'd say look into two different source ports: namely, ZDoom and GZDoom.
ZDoom is one of the most popular source ports capable of running all WADs and it's still being maintained. GZDoom is the OpenGL supported version of ZDoom with new scripting capabilities and GL lights.
For Quake 1 there's the DarkPlaces source port, and for Quake 2 there's Yamagi or Q2PRO.
(G)Zdoom can play all wads made for other ports but it's not backwards compatible with wads made for older version of zdoom. And that's a pity besides you have to change many default options to play "doom" like it was. In original doom monsters have infinite height, so you can't walk on monsters,pass under flying monsters. Looking up/down, jumping and making the bfg more powerfull are other changes. Great mods, wads and even indie games have been made with g/zdoom but the topic is the original doom movement. In that context people use mostly prboom + or chocolate doom.
Doomsday/jDoom was what I used the last time I tried to play it about five years ago. It modernizes the engine a bit so you can have modern niceties such as WASD movement and mouselook.
It even had an option to replace the sprites with 3D models, but I found I much preferred the sprites.
100% agreed. use the Doom high res texture pack for higher resolution walls and floors, but keep the sprite monsters - the 3D ones have a different art style.
High res textures really fall into the uncanny valley for me. The original low resolution textures let your brain fill in the gaps, and it's pretty good at that.
Heh, funny this should come up as just last weekend I discovered Doom Retro (doomretro.com).
It has a few odd non-retro options enabled by default (screen shake on impact and translucent firey projectiles being the main ones that annoyed me, but they're easy enough to disable) but other than this is probably the closest to a "pure" DOOM experience I've had on a modern OS - not counting DOSBOX of course.
There are a ton of quake clients, some that are very minimal (and just try to fix bugs and support new machines), and some that add or enhance new features or engine effects. There are also some that are built with competitive multiplayer in mind. My two favorite are Fitzquake and Fisheye Quake.
Also you might want to check out http://celephais.net/board/news.php which has a ton of very high quality user content for additional chapters, like mini expansion packs. Some really great level designers and artist who are making still making stuff for this game.
There are lots of alternative engines for the games as well. I have to re-research them every time I get an urge to play, so I, too, would be interested in anyone with an opinion one way or another to chime in with their preferred approach.
For ultra purity, there's basically only Chocolate Doom (or DOSbox and the original game). For modern features (but losing the Doom "feel"), (G)Zdoom or Doomsday; for stuff in the middle, Doomretro, Crispy Doom, Prboom+, Eternity.
I'd say Crispy Doom (or Doomretro on Windows) are good balances.
If you insist on using your CD rather than using a GOG or Steam copy, you'll want to be able to get at a "doom.wad" file. Depending on the CD you have, it'll either be available as a regular file, or compressed as an LHA archive. In the latter case, you'll find either one file such as "RESOURCE.1" which you can extract directly with lhasa, or several files like "DOOM_SE.1", "DOOM_SE.2", etc, in which you'll want to cat them all together into a new "DOOM_SE.lha" file and then extract that.