OK, a few months ago I had another heavy session of Skyrim, but unlike most times went nuts with the mods. I threw everything and the kitchen sink at it. The idea was to make things as different as possible, and while playing I wouldn't necessarily know whether something unfamiliar was something from a mod, something from the Anniversary Edition inclusions, something I hadn't seen in vanilla before, or something I'd just forgotten. A lot of times it ended up more obvious than that, but oh well.
Within a category I'll list them in alphabetical order, because that's the way I'm browsing through the ones I tracked. For simplicity, using the categories as Nexus Mods has them.
Necessities
There are a few things that might as well be called super-mods. They allow new kinds of interactions with the game such that many many mods have one or more of them as a requirement. For simplicity I largely ignored these before, but since this time I was going mod-heavy that wasn't really an option. They're not really that scary once installed, main thing is after SKSE64 you'll need to launch through its EXE rather than the default Skyrim one.
SkyUI. Changes up the menus, displays a lot more information.
Skyrim Script Extender (SKSE64). It uhh... does stuff that the end user can't really see, but other mods LOVE it.
Address Library for SKSE Plugins. Mods love SKSE and some of those also... love this?
MCM Helper. MCM for Mod Configuration Menus, so basically you'll need this if you want to properly access the settings for a lot of other mods.
Player Homes
Pass. I thought it would be kind of amusing to have a bunch of homes all over the map, but... homes aren't that fun for me. I just need a place to safely store my junk and have access to some thing like alchemy and enchanting, and the existing options cover that. So having like... absurd mansions outside of Riverwood just made for a weirder looking environment with little gain.
User Interface
A Quality World Map. Nice. A map detailed enough it made road travel more worthwhile. Rather than just knowing "Gotta go northeast", it's easy to check the map and know "OK, I can take this road north, then take a right where it splits."
Lor-Based Loading Screens. Like the title says. Just adds more variety to what is shown during the loading screen, along with information or quotes from the world of Elder Scrolls.
TrueHUD - HUD Additions. I only used this one a bit later, but it's pretty interesting. More bars floating on screen for things like enemies' health, plus change how you like your own bars displayed.
Unread Books Glow SSE. Like the title says. Useful to see which things on the shelf you haven't checked out before.
Vendor Sale Delay SSE. Tired of having to listen to stuff like "Some may call this junk. ME, I call them treasures..." every time before you can actually start your business at a business? This mod lets you get down to business.
Gameplay
Alternate Start - Live Another Life - SSE. This is great if you've already started the game a few times before. Rather than going through the standard beginning Helgen sequence before letting free into the world, you can start as... something else. All the starts are simple things. Don't expect cutscenes, just a different start location and items, a suggestion of who you are. There are even mods for this mod, that just add more possible starts. This go around I started as a beggar in Riften. So I just started with some ratty clothes and a place to sleep and that's about it.
Cutting Room Floor - SSE. Another part of my wish to fill the game with things I hadn't seen before. This tries to add back to the game some things that were partially completed and found in game files, but ultimately left out of the game. So a weird case of being content from the original game makers, but content they ultimately decided against for whatever reason.
Run For Your Lives. A little one I've been using even on previous playthroughs. Basically, if something like a dragon or vampire attacks a town... the folks who aren't soldiers run for safety.
New Locations
In general this is something that was a bit of a disappointment. I was kind of hoping I'd end up spending most of my time in new locations, but... most of them just weren't that interesting. Some that might've been decent as just "lands", but if it's not also full of interesting NPCs and quests, so what?
Beyond Skyrim - Bruma SE. The first alphabetically and easily the best of what I checked out. "Beyond Skyrim" is a sort of alliance of modmakers working on various additional lands of Tamriel and sharing resources, but Bruma is the only one that's been released. It takes place in the Bruma region that was in the north of the playable area in Oblivion, but a few centuries later. It meshes well with the rest of Skyrim, there's a lot of voice work, and unlike a lot of mods the voice work is pretty good, too. It still stands out as different when you're hearing all new voices rather than familiar Skyrim actors in role #5, but there's little getting around that.
The Shire SE. Honestly, as a land this one is pretty boring. Way too many big empty areas, and... it's Middle Earth, so it's totally disconnected from Skyrim and the items there have some crazy properties that are way imbalanced compared to main game stuff. So why is this on my recommended list? It also adds a Halfing race to the game and that's what I played as.
Followers & Companions
Amazing Follower Tweaks SE. I didn't use the vast majority of what this offers, but I used it for handling multiple followers and changing where they went home to when not with me, and for that it did well.
Really, the problem with multiple followers and some of the ones I'm recommending next is that... they don't like to shut up. So it's common enough for them to talk over each other, or in some cases try doing their pratter when a cutscene is starting. Some of the following actually enhance each other, though, as they were made to detect other popular mod followers and have special comments or conversations.
Inigo. Very nice. A lot of the followers feel like they don't totally fit in with Skyrim (at least unless you've modded it heavily a certain way), but he does. And he has a lot to say keeping things interesting. Also I just like thief khajit.
Lucien. Another that visually fits in and has a lot to say. He's a scholar, so the idea is kind of a reverse of the standard in that he's hiring YOU to help take him around the dangerous places full of fascinating artifacts.
Sofia. Sticks out more than the previous two, but she's pretty funny.
Vilja. Another one that graphically sticks out, but oh well. Maybe the most complicated followers, LOTS of interactions and options, and a very large quest that happens in drips throughout a normal play. This is actually sort of a sequel to a similar Oblivion mod, with this Skyrim character being a descendant. Terry Pratchett did some work on this mod, and more on its predecessor, and reading about that weird fact is really what got me searching through these mods some months back.
Environmental
Convenient Bridges BETA - Special Edition. I have frequently built bridges in games that allow such things, so this felt aimed right at me. It just... adds some simple bridges across rivers and other bodies of water where it can be convenient. Another similar mod: Northern Marsh Bridges.
Models & Textures
There are some that just take standard game textures and clean/upscale them using modern techniques for better results. Creation Club Anniversary Cleaned and Upscaled. Skyrim Special Edition Upscaled Textures.
Some provide new models/textures for items used throughout the world. Forgotten Retex Project. Glorious Doors of Skyrim SE. HD Photorealistic Ivy. High Poly Project. Skyrim 3D Trees and Plants. Static Mesh Improvement Mod.
Visuals & Graphics
Enhanced Lights and FX. Tweaks things a bit to make lights more realistic and moody. If it's a light in game, it acts as a proper light source for making shadows etc. I think this mod was also to blame for some weird effects like torches giving lens flare, but it seemed mostly good.
Lanterns of Skyrim II. This is one of those mods the first time I saw I wondered what would make someone care much about this. But... it really is a cool addition that changes the world a lot. Having new and proper lightsources around the world is pretty helpful for night activities.
Immersion
Extended Encounters. Just adds more to the set of random little events you can run across in the world to keep things interesting.
Relationship Dialogue Overhaul - RDO SE. Another I barely scratched the surface of what it offers. But it lets you target an NPC and change settings. Are they friendly? Can they be recruited as a companion? Etc. The name comes more from the fact that they've made sure all these NPCs have appropriate follower things to say, largely thanks to so many NPCs sharing voices with each other.
Bug Fixes
First Person Camera Height Fix. I played with a nonstandard race with a shorter-than-standard height this time, but by default when in first person I was still looking around from average man height. This helped make me feel properly short.
Unofficial Skyrim Special Edition Patch. Oldie and a goodie, patching lots of little mistakes Bethesda left behind. Unofficial SKyrim Creation Club Content Patches further fixes the newer content from Creation Club that's also included with Anniversary Edition.
Quest and Adventures
Helgen Reborn. It ended up being a bit shorter than I thought it would be--it's no DLC-sized adventure for sure--but still a good addition. Basically, rather than Helgen staying a bandit-infested burnt mess, it later becomes possible to assist in its rebuilding.
Immersive World Encounters, Final SE. This is a lot like the Extended Encounters mod earlier, with the difference being... it is in a different category. But more random events is good.
Magic - Spells & Enchantments
Pull Mastery Hookshot or Grappling Hook. This can be overpowered, but if you've Skyrimmed to death already, who cares? Gives you access to some spells that can either pull you toward something you target, or vice-versa. Not exactly as smooth as Just Cause, but it'll help you go from roof to roof.
This is Ragdoll - Fus Ro Dah for Trolls. Mostly this one is silly fun. Lets you knock people around like with Fus Ro Dah, but without it counting as an attack.
Audio
Sounds of Skyrim Complete SE. Adds new background noises mostly appropriate for wherever you are. Can be weird when you hear cats in town and there basically aren't pet cats in Skyrim, but on the whole the game starts to feel empty without it.
Utilities
BethINI. This program will work with a lot of Elder Scrolls and Fallout games. Basically allows you to play with most of the options you normally have to go into the INI files to get to, for settings not found in the standard launcher.
Skyrim SE Display Tweaks. Mostly a simple way to not have the game physics locked to 60fps, plus some other stuff.
NPC
Travellers of Skyrim - Travelers SSE. Adds more generic people traveling the roads. Usually you can interact with them to buy things or hire them, if you don't already have enough followers.
Items and Objects
Wearable Lanterns. Basically, adds the possibility to hang a little light source off of yourself and companions, lessening the need for torches in dark areas.
Miscellaneous
Rich Skyrim Merchants. This is a bit of a cheat, but oh well. Gives all merchants more money, so it's easier to make money selling stuff without having to run to ten different merchants to find some who have enough coin to give you. Has download options for 2x, 5x, or 10x.
ELSEWHERE
Open Cities Skyrim. This one is no longer on Nexus due to I think one of the dramas about people being unhappy with how Nexus does things. But anyway, I love having my big cities being part of the big open world, rather than having big doors forcing loading screens in and out. It can be an extra hassle if you really don't care, though. Some mods will have secondary mods that act as fixes for how they must interact with the Open Cities version of the worldspace rather than the original.