To me, Quake is one of the greatest videogames of all time. It never grows old, and even recently got remastered. But for those of us who prefer more "vanilla" experiences and can detect subtle differences in engines re-done from scratch (don't get me wrong, they can be awesome too), id Software's old policy of releasing as opensource their id Tech engines meant that people have adapted the titles for modern times, while keeping their nature exactly as it was.
With this post I'll just list my top engines as of 2022 to enjoy the first 3 Quake games, on any major platform (Windows, Linux or Mac).
The original games
To use a modern engine, you still need the original game. You can find all three games at many online stores, but my personal preference is the DRM-free, launcher-free version: I, II, III.
The "Quake refresh" version (also known as "Quake re-release") includes additional maps and modes and slightly improved visuals, but in exchange you need use a different engine to play, quite good but not 100% equal to the old engine.
Quake
Engine: Instead of the vanilla clients, use vkQuake. This engine builds and improves on the original, so it is 100% compatible with any mod I've tested, and it is even able to run the new maps of the "refresh" re-release. It is only not capable (as of the time of writing this post at least) of using the new re-release 3D models.
Alternative: The DarkPlaces engine still uses the original Quake engine as the base (so physics and the like are still 100% accurate), but offers an improved visual experience, particularly if you go for the HD Ultra quality texture pack and the Quake Retexture/Remodel Project models and creature textures. Not so vanilla in the visual aspect this way, but quite impressive.
Extra #1: Arcane Dimensions is a "mission pack" with so many incredible maps with extra graphics and enemies and complex mechanics, that requires an advanced Quake engine because goes out of the original 3D engine limits in many ways.
Extra #2: Quaddicted Random Map is a small tool I built to pick random maps from the amazing Quaddicted site and play them. While not all of the maps are supported (some of the zip files are a mess), a lot of them work and is a lazy and fun way to try new maps each time you want to play.
Quake II
Engine: Yamagi Is a much-needed engine that only provides fixes and small upgrades, being one of the few Q2 engines compatible with most (if not all) mods. As Quake 2 has aged quite badly, I recommend installing also the Neural Upscale textures to make things less blurry.
Alternative: vkQuake 2 aims to be the equivalent to its Quake I counterpart, but sadly uses new DLLs that seem to collide with some mods, not being as compatible as Yamagi.
Extra: Quake 2 Generations: To me Quake II is the least good of the trilogy, and this mod allows you to play with the Quake I marine weapons and physics (or with DoomGuy or BJ Blazkowicz from Wolfenstein 3D, also each with their weapons). It unbalances the game a lot, but at the same time you feel like playing a big Quake I mission pack.
Quake III
Engine: Quake3e it's based on the alternative ioQuake3 engine, but with many improvements, making it the best choice to play Q3.
Alternative: ioQuake3 is an engine providing cross-platform and vastly improved options for playing Quake III: Arena and Quake III: Team Arena expansion. Fully compatible.
Extra: [HQQ] High Quality Quake texture pack provides improved visuals keeping the same original style.