What is the best villager to get emeralds from?

There is another great method but it needs multile curing of villagers.

You can buy glass from Librarians and sell glass panes to cartographers for a lot of emeralds.

Get a librarian that has emeralds-> bookshelves and books-> emeralds trades. Then, cure and infect it many times until the bookshelves cost one emerald and the books give one emerald. Then, get a book, trade for emerald, input emerald to get bookshelf, break bookshelf for 3 books, then repeat.

Clerics will trade Emeralds for Gold.

If you have a gold farm, this can be an efficient way to get Emeralds.

I like to use the Apprentice/Novice Stone Mason. They offer 1 emerald for 10 clay and also 1 emerald for 20 stone. It's a grind but worth it

I prefer to use a farmer(composter), though a fletcher(fletching table) is very useful as well.

A Fletcher villager (with it's workplace block being the fletching table) that sells sticks for emeralds is a pretty decent and cheap trade. If you're able to make a dark oak, giant spruce, or giant jungle tree farm, or you just happen to have an over-abundance of wood, then this villager will prove to be very useful.

Either novice farmer, considering wheat is pretty easy to get, or novice armorer, because coal is easy to get.