Vvardenfell is a harsh world and we love it for that. We even add mods to balance the game i.e. remove obvious exploits, and add realism. Some of us actually like the pain and install mods that make the game way more challenging.
All that is good and well, but there are mods that don't make the game easier, just a little less tedious. Here are a few of my must-have comfort mods.
Warning: Because these mods do the impossible, they typically require MWSE/MGE.

Inventory Management

• inom - Inventory mouse wheel by isNaN. I will NEVER play without this: transfer anything to and from your inventory with the mouse wheel.
• MWSE Containers by Greatness7. With this you can buy containers (duh) that look great (thank you LondonRook). Cherry on top, they are portable and some even act as sorters: ingredients, books, scrolls, potions, and ammo. Cherry on top of the cherry, even items added by mods get sorted.
• Mort's Quickloot lets you see what is in a container (unless it is locked or scripted). Also lets you empty said container in one go or alternatively, selectively pick up what you want, all that at the press of a button.

Player Management

• Merlord's Auto Ammo Equip. Does what it says on the tin - every time you run out of arrows, every time you equip a bow, every time you switch to a crossbow.
• Mg979's MCC Leveler. The love baby of Madd and GCD: as your skills improve, so do your attributes. You won't get a multiplier when you level up. The only drawback is that you need to be in/travel to Seyda Neen for the scripts to kick in. A good alternative (and a simpler mod) is Linora's leveling mod that also removes the headache of leveling up but lets you have the multipliers.
• Merlord's Quick loadouts lets you equip a whole set of gear at the press of a button, and switch to another set of gear at the press of another button.
• Remiros' Torch Hotkey or Fliggerty's older Handy Equip that lets you set up a hotkey for torches, lockpicks, and probes.
• For lockpicks and probles only, check out OperatorJack's excellent Security Enhanced.
• SuperQuail's Descriptive Shrines so you know what the blessing you are paying for it! Also adds the option to cancel and restore health.
• Apoapse's Attack so that when your attack connects... it connects! If you are in for a bigger combat overhaul, I recommend Next Gen Combat that adds loads while letting you configure the mod the way you want, directly in-game.
• Morrowind Code Patch, be sure to select swiftcasting. Arguably, this makes the game a little easier since you don't have to switch between readying a weapon and readying a spell.

Companion Management

• Merlord's Kill Command: press a key (K by default, but easily configurable in-game) that sends your companions, followers, pets, and summons to attack whoever you were looking at. No more slow ghosts floating around in circles before going poof! Also fun to use.
• Melian's Teleport Mod: never lose a companion again. Also lets you have multiple marks (more balanced with Abot's patch).
  NEW Customizable MWSE Multi Mark and Harder Recall by Virnetch does the same but offers more in-game custom options.
• NullCascade's Diligent Defenders. If you find that the Morrowind Code Patch option is not responsive enough. Personally, I am not using this anymore because I love sending my minions to kill my target with Kill Command.
• Easy Escort by NullCascade makes any follower (scripted or not) follow MUCH better.
• Abot's Take My Place to make NPCs and companions move out the way.
• Companion Health Bars MWSE by Mesafoo, to keep an eye on your comapnions'health.

UI Improvements

• NullCascade's UI Expansion. A must if you have a very large spellbook: UI Expansion lets you filter spells by school or search them by name. My favourite feature is the dialogue window: topics that don't have any new information are greyed out so you don't have to read the same rumour again. Includes an option to tranfer items faster as well.
• Greatness7's Poison Crafting lets you craft poison (duh) but it made this list because you don't need to pick up your apparatus to make potions anymore, much like the old At Home Alchemy did. It also makes potions on shelves and in your inventory easily recognisable.
• MWSE Alchemy Filter by Greatness7. In the alchemy window, lets you bring up a menu with potion effects, once you've selected one, the mod filters all your ingredients and, based on your skill, will leave the ones matching your criteria.
• Aleist3r's Clock Block adds a small clock right on top of the mini-map: fits seamlessly into the UI and ... tells the time, yours or the Nerevarine's.
• Either the Morrowind Code Patch option to add "owned" to the tooltip of owned objects, or use Pete the goat's Ownership Indicator. Admittedly, this makes the game a little easier: if you want to steal, make sure no-one sees you and ownership won't be a problem.
• NullCascade's Sophisticated Save System will autosave your game regularly. In my setup, occasionally, when my game crashed, I could not load some of the autosaves. But then again, if I have no autosave to begin with, I have nothing to load.
• Expeditous Exit by NullCascade to quit Morrowind in a second.

Getting Started

Morrowind is a harsh place and rats are deadly for a prisoner freshly off the boat. Here are a few mods to kickstart your adventures (without checking every tree stump in Seyda Neen):

• Gavrilo's Adventurer Starter Pack: a balanced solution, you buy a handy set of potions and tools all at once.
• Spuzzum's Starting Equipment is a more generous mod that will give you items and spells based on your skills (great for custom classes). The only downside is that you need to go to Seyda Neen to collect.
• Merlord's Starting Equipment does something similar, minus the spells. It will however work with any chargen mod you use.
• If you only want spells (or additionnal ones), grab Tizzo's Useful Starting Spells
• Personal Effects by R-Zero is a balanced mod where you get a set of items based on your vanilla class.
• I've already recommended Chargen Revamped Expanded Lands in a previous guide, if you want something more lighweight to skip the chargen, Quickchar is for you.

Final words

What did I miss? Let me know~
Many thanks to members of the MW discord who pointed out mods I forgot.