Spiral galaxies barred spiral galaxies and lenticular galaxies.
If you had to pick between the main types (spiral elliptical and irregular) then it would be spiral. However sometimes it is a bit more complex.
Spiral Galaxies consist of a central bulge and protruding arms. Sometimes they have two arms that connect in a bar that crosses the center and this is called a barred spiral galaxy. Lenticular galaxies are like a cross between spirals and ellipticals and are also disc-shaped.
Ellipticals are like big eggs or spheres and irregular galaxies are unclear blobs. Peculiar galaxies do not fit into any of the other categories.
Here are some useful resources on galaxy types:http://space-facts.com/galaxy-types/https://en.wikipedia.org/wiki/Lenticular_galaxyhttps://en.wikipedia.org/wiki/Peculiar_galaxy