[AntiGuv]

I recall that the Milky Way is between the b and c categories, so I'd guess an SBc going on SBb. That artist rendering would seem to have the spirals wound up too tight based on what I've read about the Milky Way before and the representations I've seen. Maybe someone more knowledgable could help out!

[LibWhacker]

Here's Hubble's own classification. SBa, SBb, SBc are barred galaxies. Sa, Sb, Sc are unbarred spirals. Looks like we're an SBa, the most tightly wound barred spiral?