Since I got my new computer I havn't installed Morrowind yet and up till recently I wasn't really very aware of the modding community so I'd love suggestions on what the best mods would be to put in with it. I also have both expansions since its the game of the year edition.

Oh boy, that's a difficult question to answer, mainly due to its length. A good place to start looking for Morrowind mods is Planet Elder Scrolls (TESNexus has a better selection of Oblivion mods though).

Wells some of the many mods (I will leave out fixes and graphic based mods) that I like that I currently have running (besides the official mods, which I also recommend) are:

Necessities of Morrowind (conflict with the Entertainer's official mod, I believe someone has made another mod to fix the conflict)
Juniper's Twin Lamps (Any Twin Lamps mod which receives high ratings will do)
Any mod from the LGNPC team
Dracondros Voice
Vampire Realism II
Morrowind Cities Unlocked
Morrowind Bandits Unlocked
Balmora Waterfall
Houses and Apartments by ashworm
Better Cursed Items (only tweak I'll recommend)
Great Shoals
any high rated mod which adds a smith to Seyda Neen
Wayfarer's Rest
any high rated mod which adds centurion archers to the enemies lists in dwemer ruins
Morrowind Comes Alive
The Neverhalls
Bob's Armory 2
any high rated mod which makes wild life less aggressive (at least to the point of not having rats suicidally charge a 40th level character)

That should be a good list to start with, I kept some mods generic since there are multiple mods which are good which do about the same thing; I recommend you look for those types which modify the game to your specific preferences.

I actually recently got Morrowind and went searching for mods. Things I look for tend to be small graphical changes, but when in-game, makes the experience more immersive. Here are some of the good ones I found. (mostly from Planet Elder Scrolls, but some are probably on TESNexus)

-Better Heads
-Better Bodies (self explanatory)
-Book Jackets, one of the first mods I got on Oblivion, something about the books having words on the cover, and pictures it's great
-Delay Assassins, for new characters which you don't want immediately involved in the Tribunal expansion (turn esp off if you are ready to start, or just strong enough to fend off DB attacks)

With these character mods, everyone looks better that the Vanilla Oblivion NPCs do, it's pretty shocking the difference.

also a few mods which add more clutter, and slightly raise prices for junk-type stuff you find. It helps in the beginning. Possibly considered a cheat, but, playing Oblivion I'm used to regaining magicka, so I also got fair magicka regen. It's not overly powered, I think depending on your Intelligence it does 1-5 mana a second.