Doom 64 is the only Doom I played to completion. I love it. Still own the cart.
Bought Doom and Doom II on Steam but haven't played yet. Found the vanilla too low-res/pixilated, and tried a couple of the popular engine mods but it didn't feel authentic to me. I think I might need the ones in D3:BFG
I mean, source ports are something of a sliding scale of authenticity.
On the "as close to vanilla as possible" end, you've got Chocolate Doom, which is basically vanilla
Doom but compiled to run on modern systems without DOSBox. There's also Crispy Doom, a Chocolate Doom variant with marginally higher resolution (640x400 instead of 320x200). One notch above those would be Chocorenderlimits, which raises some of the engine's limits for testing purposes (so you can see where you'd run into a visplane error, but keep playing through without the game immediately bombing out).
Slightly higher up, there's Boom and its variants. For this subset, I tend to go for PrBoom+, since vanilla Boom is a DOS executable, and PrBoom+ is relatively well upkept. Generally speaking, it plays like vanilla
Doom, but it's limit-removing, and has Boom-specific features like customizable linedef specials, scrollers, fake floors and such that expand level-designing capabilities significantly. Also comes bundled with GLBoom+, which is PrBoom+ with a renderer. You can enable proper mouselook in that one, although it's strictly optional, and will still play akin to vanilla
Doom if you opt not to.
On the more advanced end of source ports, you've got ZDoom, which is generally geared toward modders, with even more advanced linedef and sector specials, ACS scripting (to enable Build-esque level events), DECORATE scripting (to allow you to create custom enemies, weapons or, well, decorations), slopes, 3D floors, et cetera. GZDoom is one step above that, being a very-up-to-date OpenGL renderer for ZDoom. Zandronum is also ZDoom-based, although it's a few versions behind; you'd only really want that one for multiplayer (ie: you
will want that one, but probably wouldn't play single-player on it). If you're so inclined to see if the hype surrounding mods like
Brutal Doom are really deserved, this is the engine you'll need to be using.
There are others like Doomsday, 3DGE, Eternal Engine, Doom Legacy, but the ones in the three prior paragraphs are the only ones I tend to dabble in.