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.