It's funny coming to such thread a couple months after the OP made it, and surely already has gotten their answer and made their choice. But, in the interest of helping future people with this similar question, and because I just really love DOOM and have a whole ass setup for it I want to share, here goes:
So, just like Johnathan's post up there, I'll split them into categories, but I'll only mention the ones I actually use. There are so many source ports that you can become lost in the sauce very easily. And first of all, I have to mention the Doom *launcher* that I use: Doom Explorer. It allows me to not have to mess with ports individually and just set up the experience I want to have and launch it.
You save presets of port+wad+mods very easily on this one.
Now, for the actual ports.
Vanilla:
-Crispy Doom: It has all the crunch of the original game, but plays and looks nice on modern resolutions. I like putting an external CRT filter over this one. Good for vanilla or limit-removing wads.
Enhanced vanilla:
-DSDA-Doom: The "official" Doom port used by speedrunners, from the Doom Speed Demos Archive. It's a direct evolution of PrBoom+ with many added features that bring compatibility to modern mapping standards, and enhanced demo recordings. Can run any Doom format from limit-removing, to Boom, MBF21 or the latest ID24 standard.
-Woof! : it's an evolution of the old Doom port for Windows. Actually my favorite! I just like the way it feels, it's slightly different to DSDA. Has many nice modern features too, runs all the same mapping standards as DSDA. Whenever I'm randomly in the mood for playing custom WADs, this is the one I launch.
Both of these actually also support some mods, MBF21 particularly is a very feature rich standard that expands a lot on the old Doom formula.
Modern:
-Eternity Engine: This is
like the previous two that it plays all the old formats in a vanilla-like manner, but it also has it's own advanced feature set that allows for specific mapping tricks, like horizontally moving walls. But let's be fair here, this one isn't very popular. If you're here, you're here to play Heartland. Which is an excellent WAD that only runs here.
ZDoom derivatives:
-GZDoom: here we are. The one port 99% of the internet will tell you to play. It does NOT play AT ALL like vanilla Doom. In fact, this really is a game engine that happened to be based on playing Doom at first. 3D aiming, jumping, rounded models, it's own completely separate mapping standard and modding language. You can do amazing things in GZDoom, create wholly different games and experiences, even publish commercial games like Selaco or Hedon. Now, I do really like playing mods on GZ, you can see many presets for it on my list. But when I want to play
DOOM, this is not the port I launch. This is the port I launch when I wanna play a synthwave-drenched, high lethality, high movement shooter with custom monsters. Or when I wanna have a slow, trudging survival horror experience with creepy music. Or Sonic racing. Or Mega Man deathmatch. Not actually Doom.
Oh, and it runs complex or monster-dense maps pretty badly. I think it's impossible to complete Okuplok with this port, all the previous ones run much better.
-LZDoom: has most of the features of GZDoom up to certain updates, runs better on lower end machines. Can be helpful sometimes.
Multiplayer engines:
-ZDaemon: vanilla-like Doom deathmatch. Often very empty and deserted. Has it's own server browser.
-Zandronum: multiplayer focused fork of GZDoom. Supports many mods. Everything I said about GZ also applies here.
-Q-Zandronum: altered Zandronum that adds a Quake feel to the movement and shooting. Used as base for the
excellent Quake Champions Doom Edition mod.
-Odamex: now we're talking. Vaguely based of ZDoom, but still somehow plays very vanilla-like if you want that deathmatch or coop experience. Host of the OdaHorde mod, which is really fun if you can get into a session of that. Pick up public games can be found often.
-Choco/Crispy/Woof all also have multiplayer implementations that are just like vanilla deathmatch too.
Android ports:
-DeltaTouch: it has several ports within the app, all very configurable and playable with touch and motion controls. Just put the wads on your phone memory and enjoy.
And lastly, if you don't wanna have allllllll the trouble to go after any of those, and just wanna play some Doom. You can always go play the latest Doom+DoomII port by Nightdive Studios. It's actually running in a port that is a "cousin" to DSDA-Doom, with support for custom WADs through it's internal mod browser. It just doesn't have any of that GZDoom nonsense, but you don't really need that to enjoy Doom. Also the multiplayer is pretty good, especially now that it supports map packs too!