Hello. I just got the Anthology and plan on playing Morrowind for the first time tomorrow

Does the Morrowind disc come with the latest patch? Or is that something I need seperate?

It is the GoTY version of Morrowind, which means that it has all the official patches included.

There are two community patches also, and they should be used, since they fix and/or improve many problems.
You can find info about them near the top of http://www.gamesas.com/topic/1305729-mod-recommendations-for-new-players/ under the "essentials" header. (also has info on where to install, since Program Files is not a good place to keep your Morrowind)

Be sure to install in this order: MW->Tribunal->BM