Recommended Mods

 
Engine

Morrowind Code Patch (MCP) - Hrnchamd
https://www.nexusmods.com/morrowind/mods/19510/?
Incompatible with OpenMW
Modifies Morrowind's exe to fix bugs and optimize things. This allows you to scale up the map to show TR's landmass, but still being a fixed size.

OpenMW - OpenMW team
https://openmw.org/en/
Incompatible with MCP and MGE XE
An opensource engine replacer for Morrowind, fixing many bugs with Morrowind's engine. OpenMW allows for better performance of Tamriel Rebuilt on modern hardware. It also allows the map to be as big as your mods need it to be, at a higher resolution than MCP.

Bug fixes

Morrowind Patch Project
http://en.uesp.net/wiki/Tes3Mod:Morrowind_Patch_Project
Incompatible with Patch for Purists
"Fixes almost all of the bugs and problems with Morrowind and its expansions. While the official patches by Bethesda only fixed a couple of dozen bugs, this patch fixes several hundred. The goal of this patch is to make the game completely bug-free."

Patch for Purists
https://www.nexusmods.com/morrowind/mods/45096/?
Incompatible with Morrowind Patch Project
"Patch for Purists strives to be a all-in-one patcher for everything in the The Elder Scrolls III: Morrowind Game of the Year Edition that is considerd a bug."

Morrowind Optimization Patch - Remiros and Greatness7
https://www.nexusmods.com/morrowind/mods/45384/?
"This mod greatly improves outdoor (and to a degree indoor) performance in Morrowind, as well as fixing a lot of errors related to flora."

 
Essentials 

Delayed Dark Brotherhood attack - Kir
https://www.nexusmods.com/morrowind/mods/14891/?
"Based on original Avenger's Delayed DB Attack, this mod makes Dark Brotherhood assassins only attack player in his sleep after he reached some significant point in the main MW plot (and accordingly, decent level)."

 

Project Tamriel
http://project-tamriel.com/index.php

Skyrim: Home of the Nords - PT Team
https://www.nexusmods.com/morrowind/mods/44921/?
Adds in a portion of Skyrim into the game: the Reach near Markarth.

Province: Cyrodiil - PT Team
https://www.nexusmods.com/morrowind/mods/44922/?
Adds in the island Stirk located west of Anvil. 

Miscellaneous

MGE XE - Hrnchamd
https://www.nexusmods.com/morrowind/mods/41102/?
Incompatible with OpenMW
"Allows Morrowind to render distant views, scenery shadows, high quality shaders, UI scaling and other features." Works with the original engine, so can be combined with the Morrowind Code Patch but will not work with OpenMW.

Anthology Solstheim - Anonytroll (Atrayonis)
https://www.nexusmods.com/morrowind/mods/43436/?
Incompatible with most Solstheim mods
This mod simply moves Solstheim to a lore friendly position, away from our city Baan Malur.

Better Dialogue Font - Hrnchamd
https://www.nexusmods.com/morrowind/mods/36873/?
This mod makes Morrowind's font clearer without changing the font size.

Graphic Herbalism - ManaUser
https://www.nexusmods.com/morrowind/mods/43140/?
"It changes the way you pick plants (and some other ingredients) in the game. Instead of treating them like containers, which you must "open" to take items from it, they are more like activators - you simply activate the plant you want to harvest."

Graphic Herbalism Addons - Anonytroll (Atrayonis)
https://www.nexusmods.com/morrowind/mods/43829/?
You must have Graphic Herbalism installed for this mod to work!
An addon to be used with Graphic Herbalism, which allows the same functionality for containers present in Tamriel_Data.