I would not recommend Morroblivion unless you really can't stand the way Morrowind plays, as then you lose access to many outstanding Morrowind mods. Also, you're probably best off only starting with graphics mods and patches for your first time through, as gameplay altering mods more often than not make the game harder, and it's good to have some experience with vanilla so you know what you want to mod.
Anyway, for mods that you should have (this is by no means a complete list)
Morrowind Code Patch (http://morrowind.nexusmods.com/mods/19510/). Fixes many bugs with the game, most importantly many of the causes of save game corruption, and adds a few nice features (such as Oblivion-style spell casting). A must use.
Morrowind Patch Project (http://www.sendspace.com/file/mmaydw). Fixes many problems that can be fixed with the game's mod tools, such as scripting bugs and spelling errors. Completely compatible with MCP, and they should be used together.
Morrowind Overhaul - Sounds and Graphics (http://planetelderscrolls.gamespy.com/View.php?view=Mods.Detail&id=8987/). Essentially a compilation of most of the best graphics mods for Morrowind, and does include the two mods I listed above. If you don't want the whole package, there is a list of all the mods in it with descriptions and links, so you can choose what you want. Warning: large download.
GCD (http://planetelderscrolls.gamespy.com/View.php?view=Mods.Detail&id=2030). Changes the leveling system, eliminating lots of the annoyances with it. One of the few gameplay-altering mods I would recommend for first-time players. Also adds a very slow Magika regeneration, and makes stealth and magic characters much easier at low levels.
BTB's Game Improvements (http://planetelderscrolls.gamespy.com/View.php?view=Mods.Detail&id=7904). Basically rebalances just about every aspect of the game. However, it does make many aspects of the game harder, so it's not recommended for your first playthrough.
Tamriel Rebuilt (http://tamriel-rebuilt.org/). Adds a significant part of Morrowind's mainland to the game. Is in many ways higher quality than the vanilla game.
That's all I can think of right now, although I'm sure I'll be back with a few more.
