dhewm3 VS RBDOOM-3-BFG

The installation is different from what you might be used to from your typical mod. Download dhewm3_1.5.2_win32.zip from the githup page, unzip it, then copy, as instructed by the WHAT_TO_DO.txt files in the base and d3xp directories of the unzipped mod the .pk4 files from the game directory over (d3xp is only there if you installed the Resurrection of Evil add-on first). You can then uninstall the game from Steam.

I played through it with dhewm3 recently. Really enjoyed it.

There is a source port of Doom 3 if you want to play it on Linux or macOS.

if you are going to play it on PC, then get the original 2004 release, with the dhewm3 source port since it can get to widescreen easily and is friendlier on modern devices.

Why do you want to run old, buggy code through wine when you could use native dhewm3 to play the original (non-BFG) version of doom3 with Bugfixes, OpenAL audio and proper widescreen support? https://dhewm3.org/

for me go for the original Doom 3 + dhewm3 source port since the source port can get to widescreen easily and is friendlier on modern devices. BFG Edition aint that bad but its very easy and lacking other content that the original Doom 3 had (especially ROE) and it has less enemy count.

RBDoom3bfg, same thing, but for the BFG edition.

On the other hand BFG edition supports 120Hz rendering and has some great gamepad support. However the "shoulder lamp" and some tweaked brighter lighting destroys the game's atmosphere IMO while some textures and lights appear worse. I'd still recommend it if you liked the original game, but perhaps also play it with RBDoomBFG and its GI datapak - it introduced PBR shaders and changes the lighting considerably, but the game wasn't designed for that so i'd recommend it only for a second playthrough (you can disable most of the effects but even then it still looks off). The official BFG edition is closer to the original Doom 3 but still has its own issues so unless you want 120Hz rendering and/or gamepad support, i'd still recommend the original (with Dhewm3). Also note that the original BFG edition doesn't allow you to skip cutscenes which is annoying for a second playthrough.

BFG has better out of the box support, but both versions are open source and as such the community has made source ports for both of them to the point they are essentially equivalent and you only pick the one with the features you want the most, last time I played was using BFG because RBDOOM3 added support for PBR so the game isn't so absurdly dark but your mileage may vary and may prefer dhewm3's more faithful experience using the original release