(New Quake 2021 Update) How to get Quake to feel and play like it should!

First, I'd recommend trying to change the renderer.

In the launch options of your game (Right-click in Steam library -> Properties -> Text box at the bottom), add this command:

+r_rhirenderfamily "d3d11"

This will render the game in DirectX 11. If this doesn't work for you, you can return to the default Vulkan renderer with

+r_rhirenderfamily "vulkan"

If this doesn't help your stuttering, or your game is crashing with these launch commands:

Go into Options -> Open Video Settings... in game. Disable Vertical Sync in video settings, and set Window Mode to Borderless. Then, go back and set Max FPS to Unlimited. If you are getting noticeable screen-tearing, cap your FPS with NVidia Control Panel or any applicable program.

(Note: I've had to repeat this step on rare occasion when re-opening the game for some reason, by enabling V-Sync and disabling it again.)

There may be another fix to the game feeling off that you may attribute to stuttering, which I'll detail below.

Any people who have played Quake 1 in other forms before (or just notice awkward movement in general!) may have noticed the player speed is off. This makes it difficult to strafe jump. There are commands to help remedy this. (Please make these default in an update soon, Bethesda!)

Open the in-game console with the ~ key, and input these three commands:

cl_forwardspeed 400
cl_sidespeed 350
cl_backspeed 400

They should save even between game restarts. If not, you can add them to launch options in the same format as the renderers above.

If you end up having issues with movement in multiplayer, or want to return to the original movement settings, these are the default values as of the launch version of this port:

cl_forwardspeed 400
cl_sidespeed 350
cl_backspeed 200

If your game looks blurrier to you than it should, or the colors are muddy, I recommend turning
Texture Smoothing and Antialiasing to OFF.

The AA solution in this port just blurs the whole screen, and Texture Smoothing (which is on by default) blurs the floor textures and makes them look super muddy. Everything is a lot crisper with them switched off. Also, changing Fog, Depth of Field, and Ambient Occlusion to OFF may help as well.

Note for Quake 64:
Quake 64 has a built-in CRT filter.
You can disable this with r_crtmode 0 in the console with the mod loaded.

There's a few settings you can modify to make the game feel a little closer to the original.

In original Quake, nearly all of the graphics options in the menu would be turned off, but some of my favorites for preservation are these (besides ones already mentioned above in fixing Blurry Visuals):

Display:
Model Interpolation: OFF - Removes the "smoothness" with animations. Original Quake's software renderer only showed keyframes, making them look choppy. The game was designed with this in mind, and I think it looks better this way!

Enhanced Models: OFF (optional) - Disables the new models included in this version, replacing them with the old ones. These new ones still look great though, so it's up to you!

Gameplay:
View Bob: ON - Original Quake had the infamous view-bobbing on. It's crazy to me that this is off by default in this re-release, I feel like this is trademark Quake!

HUD Style: Standard/Full - Whenever I used to play Quake, I used the "standard" setting just because I didn't like the lower screen space of the weapon counter. Also interesting that Minimal is on by default instead of the classic HUD, but honestly as a longer-time player I think I enjoy Minimal more. However, just like DooM 1 & 2, the full HUD with the face and all is the original version. Pick what you like!

Show Classic Quit Prompt: ON - Why is this off by default? lol

Console (open with ~):
Disable water filter - Enter the following command in the console:
r_renderwaterviewfx 0
(Removes the new water filter when looking underwater.)