I’ve used Mod Organizer 2 successfully, and is the one I would recommend (for Skyrim, never tried modding Morrowind and Oblivion). Have Steam launch MO2, have MO2 launch Skyrim. Also works with Fallout 4 modding.

I’ve made Wrye Bash work both natively in Linux and via WINE before, as it’s in Python. However, it wasn’t easy – it didn’t work out of the box, and I had to both apply patches and hand-modify some of its filesystem code – and was becoming more problematic on HEAD in git. I don’t know if the situation has improved since then. I consistently saw a certain level of breakage with the wxWindows widgets that it used – had controls operate flakily and such.

I don’t recommend manual installation of mods in general; it’s a pain to manage. You want a mod manager.

A few things – most notably SKSE – do require manual installation, as they aren’t packaged in a “mod” zip that MO2 recognizes; the executable should go in the top-level game directory. SKSE does work.

If you’re running Bodyslide to regenerate clothing models, run that through Mod Organizer 2 as well.

If you modify animations, IIRC I wasn’t able to get Nemesis working; I did have luck with FNIS.

I have never attempted to get ENB shaders working, so I can’t say whether-or-not that works on Linux.

Setting up a modded install is still – depending upon the scope of what you want to do – a major project, but the challenges in tracking down mod incompatibility issues isn’t really Linux specific. If you go install a couple hundred mods, you’re going to have a broken installation. I would set aside some time for this. I also used binary-search shooting – if your install isn’t working, disable the second half of your mod list. If it still isn’t working, then disable the second half of the first half of your mods and repeat, etc. That’ll find a problematic mod in time logarithmic in the number of mods you have.

EDIT: If you want to run Morrowind in Linux, you may want to run the open-source engine reimplementation OpenMW, which is a lot-more-capable than original game. I played Morrowind on OpenMW, and the mods I used worked there (though damned if I can remember how I managed them, but I don’t recall it being a hassle).

EDIT2: I was able to get browser links working with Linux-native browsers using the nxm: links on Nexus, having Mod Organizer 2 handle said links to download and install mods, which I found to be the most-amenable way to do so.

EDIT3: You may want to use the latest Glorious Eggroll build of Proton. I distinctly remember some issues that there was some patch to work around involving heap memory allocation that Valve’s Proton builds didn’t handle at some point and Glorious Eggroll did, though I can’t recall whether that was both Skyrim or Fallout 4 that smacked into it.

EDIT4: I don’t recall whether I used modorganizer2-linux-installer for the whole thing at the end, but I am sure that the nxm link handler I used, modorganizer2-nxm-broker.sh, came from there. That’s probably the first thing that I’d run, as it’s intended to be a one-script setup for a Mod Organizer 2/Skyrim setup in Linux. If it works, great, you’re mostly done with the setup (just need to manually install SKSE, which I don’t believe it installs).