I'm not sure it has to be story-focused really, just be about more than shooting and finding keys.

I have no idea what the first FPS with emphasis on story was, but I do recommend already mentioned Clive Barker's Undying and No One Lives Forever (though that one is 80% stealth 20% shooter).

Edit:
F.E.A.R. games also have an interesting narrative, but in terms of gameplay 95% of the game is shooting stuff. From the original post I would say that is not what StingingVelvet is looking for, at least on Heretic 1 part.
Heretic is essentially a Doom clone in different setting with some nice details added (inventory and flying), but fundamentally it plays exactly like Doom. Hexen is a bit different and heavy on exploration, but in principle isn't all that different from Quake 2 in terms of design and there really isn't that much story. Hexen 2 may be an interesting middle ground though. Funny thing is, there are elements in both these games that I like and can't stand. I am one of (very few from my observations) people who liked gameplay and design of Q2 much better than Q1. I loved the hub system, I felt the guns felt better, levels were more open etc. But for some reason they decided to put it in the most bland setting imaginable. Q1 I think had the best atmosphere out of all id games. The setting was great, the music was great, but I always feel there was something missing in the gameplay department.
I would love to see a return to that Lovecraftain setting, preferably with a more serious tone and not the Doom goofiness.

Probably a reasonable assessment. The main issue is that a lot of the older stuff, especially when it came to FPS was rather singular-minded in focus and often, to a possible detriment, trying to replicate what was previously successful so the industry got a lot of clone of x scenarios because it's where the money was.

Ultimately it all depends on what he's looking to try out and/or revisit as the case warrants. He certainly isn't lacking for options though.

Most of the games mentioned I've already played, which I expected. That's why I made kind of a hybrid thread also discussing when the story and immersive elements of first-person games began, and which were early highlights.

It's nice to get recommendations for stuff I actually haven't played though, like Strife and Tron.

I have yet to play Strife, but TRON 2.0 is definitely a must-play. Amazing game. I would recommend to use the inofficial patch "Killer App" (https://www.moddb.com/mods/killer-app), which allows for widescreen and fixes numerous bugs.

Edit.

I hate the whole "RPG elements" that gets thrown around so much these days. Just call them what they are: stats. They were around way longer in a variety of games before that stupid moniker even existed.

- Another vote for Strife (1996) here then. It had mechanics like side-quests and multiple endings all whilst being written on the 1993 Doom Engine. Technically Heretic & Hexen had "inventories" but were more pure "maze shooters" like Doom. Strife does actually feel a little different to play than all the other Doom Engine games.

- Hedon is a lot closer to Strife than Doom / Heretic / Hexen, and although a new game I included it as it very much feels "real old-school" simply for being a genuine Doom Engine game, so that might be worth a look.

- Aside from the obvious Deus Ex / Half Life / System Shock, if you can stretch 90s games to include the year 2000, then games with heavier story-focussed gameplay could include No One Lives Forever & Giants Citizens Kabuto, though I wouldn't call them RPG's. The bulk of the usual recommended ones (Bioshock, original Prey. etc) were all 2000's.

Wolfenstein (2009)* and probably all the later ones in the series, starting with Return to Castle Wolfenstein. I'm not sure about that last one... too long ago, I don't remember it that well....

Maybe nobody mentioned them because the first ones from the early 90s were just plain shooters?

*Side missions, NPCs, a hub city to explore, Nazi communication to read, weapons to upgrade, magical powers, puzzles, secrets, a cool silly story and cheesy acting (I don't mean in a bad way), ...

Not too much on the story section, but pretty much, everything else you mentioned...

I recommend to you Cybermage. Great exploration if you are up to it, quite dangerous and rewarding. Gloom environments, nice graphics even for DOS, one of the first shooters to have vehicles too! You can spend money in shops to buy weapons, listen to NPCs, there is even the occasional eye-candy!

You certainly cannot go wrong with that one. WIsh GOG had it.

Giants is third person though, isn't it, not FPS?

There's a "Toggle First Person" button in-game, so you can play as either.

I replayed Return to Castle Wolfenstein last year sometime and it was enjoyable but not as great as I remembered it being. Probably because yeah, it has some cutscenes and notes scattered around but is mostly focused on pure "maze shooting." Wolfenstein 2009 has a lot more to it, and I think that game is very underrated.

Can't speak for anyone else, but I could recall him previously mentioning his thoughts about the rebooted games in the series so I just took it for granted that he'd likely played most, if not all, of the rest as well.

Now that we've brought it up though, I'd sell the child I don't have for someone - I don't care if it's GOG or Steam or Bethesda's own store - to sell Wolfenstein 2009 again. I still firmly believe Bethesda would much rather people forget it and focus on the reboot titles for all their modern Wolfenstein needs though, which is a monumental shame.

Activision funded it and own the studio that developed it, so I think there might be issues there with Bethesda. Who knows though. Luckily I have a backup copy.