Well, some goths define gothicism exclusively by the music; gothic rock/darkwave etc IS goth to them, so to properly call yourself a goth, you would need to at very least be acquainted with gothic bands. I personally see being gothic as internal and the music as more to the sidelines.
I like lots of metal as well, but my musical tastes are very varied. When I first came here, I was given this link:
https://www.gothic.net/boards/showthread.php?t=5866
It'll list a ton of gothic bands, each (at least in the initial post) with a link to a youtube video. Check it out. Oh, and you might be surprised at what some gothic bands sound like; their darkness is sometimes much more apparent in their lyrics than their melodies. In fact, a lot of gothic rock sounds fairly upbeat.