I'll think of things later, but for now, I gotta say that I really like your taste. The best old skool shooters around, spiced up with just about the best indie games on the planet.
For now, I can only mention what you most likely already know: half life 2 and that free-to-play unreal tournament that epic somewhat abandoned for fortnite (but that's still pretty darn good).
EDIT: okay...let's see...
@FAST6191 gave some very good mentions.
* Serious Sam (1 and 2...probably 3 as well, but haven't played it yet) are carnage in the old "one vs all" style of the original doom. Enemies aren't too smart, but they make up for that by having massive numbers
* Duke Nukem 3D is pretty old, but not bad. in fact, they recently re-released it with an entire new episode. Probably to make people forget about DN forever, but still...I'd pick this up if you have somehow missed it
* painkiller. Not as iconic as the previous two, but a rock solid shooter in all aspects.
* rise of the triads is a "maybe". It had some pretty wonky ideas, so your mileage may vary. it had a reboot as well, IIRC
* shadow warrior: pretty much the opposite. I've played the original a bit, but was underwhelmed (note: this hasn't aged well). However, the reboot was surprisingly fun. It's from the makers of hard reset, and they really upped their game on this title. It's pretty much popcorn material, but hey...
* bioshock. TBH, this is more a sort of RPG game (with horror mixed in) than a shooter, but it's a classic for all the right reasons.
* unreal gold. since you have UT99 and UT2004, you probably know this one, but this rather classic adventure still holds up pretty well. The gold edition contains the Return to Na Pali expansion (which adds EVEN MORE levels). To me, unreal was (and still is) always better than half life 1. And that isn't to demean half life 1 in any way. If you haven't played this game yet, then I'd put it as direct priority.
* devil daggers: this is an indie game, and while it borrows a lot (nearly everything) from the classic run 'n gun doom clones, it is important to stress this: THERE ARE NO WALLS. It's just you on a peak in darkness and have to survive for as long as possible.