Since everyone's saying pretty much the same thing, I'll chime in to just to agree.
Legacy of Rome and Sword of Islam are must haves, I think. Rome I wouldn't even consider playing without. Islam is very well done. Personally, although I bought SoI when it came out I didn't play as a Muslim dynasty until recently. I'm glad I did. That pack is really impressive creating unique dynamics for Muslim houses. It's a great experience if you like the game.
I never play without ruler designer. I always create my own dynasty because I like to have real ownership of my little empire. Some people prefer to play a historical dynasty. Know which one you are. If you're like me, this is also a must have.
I love Sunset Invasion. I really throws a great challenge at the player mid-game. But if you're newer, you can put this off for now because you just get to know the base game first. But if you keep playing, I would eventually get this so you may want to pay it now on sale and just leave it disabled for a while.
As for the cosmetic packs, I think all the portrait packs are pretty essential. It gives the different characters in the game much more personality. You don't want everyone around the map looking like clones, do you? You want Mongols to be Asian, Africans to be African, and Russians to look like Tolstoy characters don't you?
I think the sprites you can mostly pass on if you want to. You tend to look at the map zoomed out and miss the detail anyway. I like them, but I don't know if I would really notice if they were gone.
The music is great. But it's pretty expensive and most packs only play in limited situations or with certain cultured characters. Plus I often listen to my own music when I play. A lot of people really love it. Go to Youtube, listen to some of it, and decide if it's worth the money to you.