Originally Answered: What exactly is Goth music? First generation goth's please help this babybat?
I'm not and elder goth per se, but my husband is and I'm not a spring chicken myself. Not sure what info you're looking for, but here's a bit of info.
Of the bands you like, Bauhaus, Sisters of Mercy, and Siouxie (Face to Face is a great song, I agree, but its among their most recent stuff) are old school gothic music. The Cure are a bit on the pop side, but I don't know of any goths who hate them for it. Other old school goth you might like: the Mission UK, Joy Division, or any of Peter Murphy or Daniel Ash's other bands.
Most of the other bands you listed would not be considered goth by older goths, although they are goth inspired. After the mid-80s, the gothic genre diverged into several different sub-genres. The genre that most resembles the original goth music is called darkwave, and includes bands like the Cruxshadows and Ego Likeness. Than there is industrial, with bands like VNV Nation and Android Lust. There is ethereal music, like Black Tape for a Blue Girl and Mira. And there's goth-a-billy, ambient, goth-punk, and electronica. My favorite are hold-overs from the late 80s/early 90s that still have a lot of old-school edge, but are more in tune with my musical sensibilities, bands like Faith & the Muse, Mephisto Waltz, and Switchblade Symphony (not still together, but their stuff is still classic).
I hope that helped a little. Its good that you asked, we were all babybats at one point.