The "Milky Way" is the name given to the galaxy in which we reside. The Milky Way is classified as a barred spiral galaxy type; a spiral galaxy with a central bar shaped structure composed of stars. The main galaxy classifications are spiral, elliptical and irregular .
Messier 32 is a dwarf elliptical galaxy about 2.65 million light years away in the constellation Andromeda Maffei 1 is a giant elliptical galaxy in the constellation about 10 billion light years away in the constellation Cassiopeia. It is the closest giant elliptical galaxy to the Milky Way
The most common type of galaxy is a dwarf elliptical galaxy. If you classify a dwarf galaxy as a galaxy, then that is your answer, however, if you don't, then a spiral galaxy will be the answer. See the related question for more details.