If you want to make this as easy as possible, then just download Revision and disable all of the mod's horrendous tweaks and changes. It's not identical to vanilla unfortunately as there are plenty of minor differences that can't be disabled, such as the crappy loading screens, but it is undeniably the quickest and easiest way to play somewhat vanilla Deus Ex smoothly. Revision can be downloaded on the Steam client itself through the Steam store. If you want genuine vanilla, then read on.

1. First thing first, you want to download the Deus Ex Map Fix. This patch fixes bugs in the most recently patched version of the game (installed on Steam by default): https://www.dxm.be/host/files/DeusEx_MapsPatch13.exe
To install the Map Fix, run the .exe and follow the instructions, choosing your Deus Ex game folder when asked. To find this folder, right click on Deus Ex in your Steam library. Go to properties, then browse local files. Copy/paste the location from the text at the top of the window into where the Map Fix is asking you to, then run the .exe.

2. Next, I recommend downloading Kentie's Launcher. This launcher fixes more bugs and allows us to easily tweak a few important options: https://kentie.net/article/dxguide/
To install Kentie's Launcher, open the file with a .zip program, such as Winrar, and copy all contained files into your Deus Ex game folder's Systems folder. Overwrite when asked.

3. I also recommend downloading Confix, which features some dialogue coding so conversations more correctly align with actions, as well as a number of typos. Please read the mod’s summary. Again, all that needs to be done is to drag all of the file’s contents into your Systems folder: https://www.moddb.com/mods/confix/downloads/lddpconfix

4. Finally, I recommend installing the OpenGL renderer. This renderer aids modern platforms greatly. It fixes countless issues that the game's outdated, default renderers use. There are various other custom renderers that improve performance too, but for me, OpenGL is the preferred option and I have tried most of them if not all, as it has the best looking lighting (clean and vanilla) and runs well: https://www.cwdohnal.com/utglr/
To install the OpenGL renderer, open the file with a .zip program, such as Winrar. Choose the Deus Ex folder and copy all contained files into your Deus Ex game folder's Systems folder.
Direct3D10 and 9 used to be the optimal renderers but it seems that modern Windows no longer supports them.

Note: All files downloaded are virus free. I've installed them for over a decade on various computers without any issues. You can delete the downloaded files after installing.

To open Kentie's Launcher, simply run the game on Steam. It will open every time. Go to configure. I will detail every option, but most can be ignored, so only deal with the important options if you're not interested in the superfluous.

The important options:
1. Under video options, set renderer to OpenGL.

2. Set the FPS limit to anything below 201. Anything above causes the game to run too fast (there's a separate guide to fix this).

If you don't know what to set it to, simply set it to 120.

3. Under resolution, pick common then choose your desired resolution. Most screens use 1080p, so use 1920x1080 if you don't know which to pick, unless you have a 4K/UHD screen, in which case pick 3840x2160. 2K screens use 2560x1440. If you're struggling for performance, then choose 1280x720 or 1024x768.

4. Under field of view, I recommend setting this to Automatic. Automatic adjusts the field of view so that it looks normal regardless of your aspect ratio. This option should be fine for most people. If you want it smaller, then 80 is likely as low as you want to go. If you want it larger, then I don't recommend using anything above 100 as it distorts the weapons/view models (there's a separate guide available to fix this - not mine). I personally play at 100 or 95.

The bonus options:
1. Under UI, I recommend enabling raw input. This makes the mouse movement feel smoother.

2. Under UI, enable widescreen cinematic subtitle fix, unless you're playing at 4:3. If you don't know which to pick, enable it.

3. Under UI, choose use custom UI scaling 1x if you're playing at 1080p or 1440p. Choose 2x if you're playing at 4K. If you're playing at lower resolutions, leave the option disabled. If you want the HUD larger or smaller than what I recommend, feel free to experiment.

4. Audio settings are above my head, so I recommend not touching them.

5. Under misc. there's an option to use single CPU. I can't imagine this will change much, so probably best not to touch it and leave it enabled as it is by default.

6. Under quality, enable 32 bit colour and detailed textures. There's no reason not to unless you purposely want your game to look worse.

7. Under viewport, choose your desired game window size.

Deus Ex's default control scheme is slightly archaic. To modernise it, here's what I pick, but remember: it's all personal preference.

1. Go to options, then controls. Enable toggle crouch. Enable toggle running.

2. Go to keyboard and mouse.

3:
Set crouch = C
Lean left = B
Lean right = N
Toggle laser sight = V
Toggle scope = mouse wheel click
Quick save = [
Quick load = \
Walk = Shift
Reload = R
Change ammo = X

The aim of this guide has been to keep the gameplay and visuals as vanilla yet appealing as possible. If you don't want to do that, then here are a couple things you can do:

1. New Vision 2.0: 2.0 is a custom texture mod for the world. It looks okay and is pretty faithful, but lacks the original textures' ability to become further detailed the closer you get.

2. New Vision 1.0: 1.0 is actually very different. It's newer and uses AI up-scaling of the original textures rather than entirely new textures. Personally I find AI up-scaled textures to look absolutely abhorrent so I have no idea why anyone would use this, but each to their own.

3. HDTP is similar to New Vision but instead of altering world textures, it alters item and character models. It's decent, but again, I much prefer the originals.

4. GMDX: GMDX radically alters visuals and gameplay. If you want the vanilla, best Deus Ex experience, I highly recommend NOT using this mod. It is a great mod, but it isn't Deus Ex, no matter how much the author flaunts it as being similar but objectively superior. Its additions are significant and often superfluous. Save this for a future playthrough.

5. Revision: Revision lives up to its title. It's a revised version of the game, butchering the artistic vision of the original game, and massively altering gameplay and level design. It's very far removed from the original Deus Ex. There's nothing wrong with that if that's what you're into, but if you're expecting it to be a graphical remaster, it is NOT what you're looking for. Many new players mistakenly get the impression that it's simply a graphical enhancement.

That's about all that's worth mentioning outside of total overhauls. Personally, I much prefer the game without all of these.

If you're still struggling to get the game running smoothly, you may consider these options.

1. (Thank you Blitz4 for finding this solution): Setting the FPS limit to something below 200, such as 60, may improve audio issues such as stuttering and popping.

2. (Thanks TastyMond for finding this solution): Deus Ex causes stuttering on some systems. This can be solved by going into the NVIDIA Control Panel then selecting Program Settings under Manage 3D Settings. Add DeusEx (needs to be recently run to be at the top of the list) then find Low Latency Mode and set it to Ultra. You can also do this in the Global Settings.