Here are some of the starships seen in Star Trek: Discovery.
Updated Nov 05 2017

Federation Ships

Crossfield Class U.S.S. Discovery - A science vessel. It is unclear whether other science vessels are similar to Discovery, but since we have now seen that the outer portion of the saucer rotates, it seems unlikely.

Walker Class U.S.S. Shenzhou - An older vessels type. Seems like it may be a light cruiser.

Nimitz Class U.S.S. Europa - Admirals ship. This ship seems very similar to the Miranda class that would come later.

Engle Class

Shepard Class

Malachowski Class

Hoover Class

Cardenas Class

Klingon Ships

D7 Battle Cruiser

Shuttle

Bird of Prey

Battle Cruiser

Sarcophagus Ship

Veqlargh class

Qugh class Destroyer

Daspu class