When most people think of the origins of black metal, they probably think of the so-called second wave bands, mostly out of Norway (Gorgoroth, Darkthrone, Immortal, etc.). Fewer take the time to consider the bands that formed the genre in the first place.
That's probably because the first wave is so confusingly ill-defined. Most of the bands cited as first wave black metal bands aren't really black metal at all: Venom, Celtic Frost, Mercyful Fate, Sodom, etc. But there are a few true black metal bands that made the scene before the second wave arrived.
Bathory: Under the Sign of the Black Mark (1987)
Sweden's Bathory is widely considered to be the first true black metal band. Their third album, Under the Sign of the Black Mark, still showed some evidence of the thrash/proto-black metal stylings of Venom ("13 Candles", "Woman of Dark Desires"), but in many places it was easy to see that this was something truly different. The tremolo-picked riffs and shrillness of "Equimanthorn" or "Chariots of Fire" are exactly what early black metal was about. Bathory also showed the style could be epic on "Enter the Eternal Fire". The album does have some serious missteps ("Call from the Grave" has a corny lead and "13 Candles" isn't really that great), but it also has some truly excellent moments, and its influence can't be denied--especially considering nearly every black metal album to this day has an intro. I give it 4 out of 5 stars.
Black Metal in Communist States
For whatever reason, many early black metal bands came from behind the Iron Curtain. You could write a doctoral dissertation on that observation in any number of fields. The next two bands are examples of the phenomenon.
Tormentor was a band from Hungary, and you may know vocalist Attila Csihar from his work with Mayhem, Keep of Kalessin, Aborym, and Sunn O))) (among others). But Tormentor was his introduction to the world, and on Anno Domini they sound like black metal via Teutonic thrash (Kreator was originally called Tormentor). At times, they do the atmospheric keyboard thing for a more epic feel ("Elisabeth Bathory" or "Beyond") but most of the time this is straightforward black metal. And it's easily recognizable as such, although at times the solos are a bit more Maiden-esque--a positive touch, in my opinion. The production sounds awful, with the volume and balance randomly shifting and some parts just blown out from being too loud (although it was remastered later on), but despite that you can hear all the instruments throughout the album. The highlight of the album is "Tormentor I", which has an incredible riff to drive it forward. I give it 4 out of 5 stars.