By the time you have an Enchanting Table, you will probably want a room dedicated to enchanting, because of the number of bookshelves you'll want for high-level enchantments. I also find a room for brewing stands and supplies to be helpful when brewing potions en-masse, as I can set up multiple stands and move bottles from one to the other to brew base potion, ingredient, and modifier in an assembly line fashion.
Nether portals can be put in a separate room if you want them indoors, since they spawn pigmen.
Not so much rooms, but outdoors (or indoors depending on your play style), you'll want areas for each of your animals that you plan to breed. You'll want them to be easily accessible but secured from monsters so a creeper won't blow up your entire pig supply.
Depending on your base layout, you might do indoor farming, in which case, that will want to be in a dedicated room. Mushroom farms in particular clamor for their own area, due to the low-light conditions required to grow them.
(Side note: traditional mushroom farms are fairly inefficient; if you want a lot of mushrooms fast, the easier thing to do is to create a large dark room, plant a mushroom in the center, and use bone meal until you get a giant mushroom. Breaking the blocks of the giant mushroom provides lots of mushrooms, which can be used to repeat the process. This requires a room large enough to grow a giant mushroom in, and dark enough for the mushroom to be planted in the first place.)
We play multiplayer and generally share a base between multiple people, so everyone builds their own private area where they can stash their things and a bed, and then we do common areas for storing communal resources. We tend to make a "forge" and a "kitchens", each with multiple furnaces and chests so smelting, crafting, and storage can happen all in the same place. Obviously for single player you'll have less volume of stuff needing to be stored for future use, so you might not need as much specialization.
As far as order, that depends how soon you need each thing. We tend to establish the base, then grow the rooms as our main chests overflow with things. The farming and animals come early, but the enchanting table and brewing stands come late due to the need for diamonds and nether access.