Ok, I have the game of the Year edition of The Elder Scrolls: Morrowind. It comes with some expansion or other, in a honkin huge box. I’ve actually had it for quite a while, just never got around to playing it. I know Oblivion is what everyone’s playing, but I want to play this one first.
I’ve heard a lot of talk about mods for Oblivion, with some people going so far as to say the game is unplayable without mods. How about Morrowind? Are there any “must have” mods? It have any glaring flaws that only a mod can fix? Some recommendations on good mod sites would be nice too.
As with most games I’d recommend playing without mods first, so you know whether you want mods, and what parts of the game you’re experiencing are mod-related and what aren’t. Not to say you should play from start to finish without mods, just to start the game out and maybe do a quest or two. Although I use a ridiculous amount of Oblivion mods, I’ve kept my Morrowind modding to more of a minimum - I guess it doesn’t really need as much help (I still think Bethesda left Oblivion a bit of a blank canvas in some ways because they were counting on the modding community to polish the game for them, but that’s a discussion for another thread).
Anyhow, you’ll probably want something like Better Heads and maybe Better Bodies, although I’m not a personal fan of the latter, the default head and body models in Morrowind are crude at best. I understand they were going for a “different” look with them, but most people who play Morrowind agree the character models are a major detractor.
I’d also suggest grabbing some of the free plugins from Bethesda, although I’d give Siege at Firemoth a pass, as it can cause some odd problems in games. Check out the official downloads here.
The Unofficial Morrowind Patch is also fairly essential (in combination with the official patch). It fixes a lot of bugs that Bethesda never got around to.
Assuming the GOTY edition includes the Tribunal expansion, I’d suggest using a mod like Delayed Dark Brotherhood Attack which ultimately makes the Tribunal expansion start make more sense - it will occur later in your character’s life, for reasons that will become obvious once you start learning more about the Tribunal storyline.
ETA: although some of the links above are to Planet Elder Scrolls, TES: Nexus is frequently a better resource for mods. Of course, modding communities being what they are, some modders only upload to one site or another, due to various personal quirks. 
It’s been a long time since I’ve played Morrowind, but when I did play it, I played it a lot. I couldn’t play it without Better Heads and Better Bodies, as already mentioned. I had no problems with Siege at Firemoth. I had so many mods, I wish I could remember them.
Interestingly, I have Oblivion for Xbox360, so I have only played that game sans mods.
If I remember correctly - and it’s been a while - the issue with Firemoth was due to GMST entries in the mod (it’s a “dirty” mod), which cause conflicts such as certain spells not working. It’s possible some of the unofficial patches corrected this, but as far as I know no new official versions were ever released.