"Must have" mods is such a difficult thing. Mods are like food, colors, books, clothes, artwork … extremely dependent on the person.
Even some mods people might consider mandatory (UI changes, unofficial patches, AE, etc.) are not considered must have by many.
If you want what is popular must have mods … which is perhaps the only way to determine must have mods if not selecting them yourself … then just go to Nexus and sort by downloads and/or endorsements:
https://www.nexusmods.com/fallout4/mods/trendingalltime/
Or do it by category to get more selective.
As an example I have modded FO4 since it came out and have over 2000 hours in it now. My current line up has 113 plug-ins (ESP) and 232 mods. Not a single one of them is in Couch's list above (ENBoost is part of ENB files and I don't really consider it a mod … although I always play with ENB).
I would say at least 70% of all my mods are for visuals. I like the best looking game I can make it. So I spend tons of time on HR texture packs and always hunting down those small texture gems to continue to fill in gaps.
My favorite texture artist is FlaconOil - just superb job and very lore friendly:
https://www.nexusmods.com/fallout4/mods/3747
I also use some texture packs from Luxor who does a great job. Best to just browse through his list:
https://www.nexusmods.com/fallout4/users/50525966?tab=user+files
I also have packs from some other authors but not home now so can't look up the names - Stromberg, Tapioks are the author names I believe).
I have visual bug fixes (about a dozen), a variety of custom armors and just a couple weapons (like a claymore and crossbows).
Lots and lots of HR textures for weapons, armor, places, critters, etc.
I only use Vivid for his wood textures - I didn't care as much for his landscape work in FO4 or some other things as much as I liked it in Skyrim.
I go for lore friendly looks and my grass and trees reflect that.
I have a couple of companion make-over mods which are very taste based. I have some settlement building mods but none of the big ones, although I highly recommend Woodys Wasteland if you like lore friendly options … again very taste based.
I also play hard core on survival mode but I don't like overhaul mods at all so have no mods that touch difficulty, balance, or the like.
EDIT: I also use none of the mods Joxer lists. I focus on immersion, visual quality, and keeping mostly to the lore (an exception is I love the large moons made by AGreatWeight based on the Pilgrim mod … don't use Pilgrim but like his moons and use a larger than normal sized one).
I own all the DLC's and have played through the game multiple times. Just started a new one last night