Okay. If you're new to black metal, you can start off with Dimmu Borgir's
In Sorte Diaboli. It's not the best example of a typical black metal album, but it's more accessible than most black metal releases.
Death metal. Though the genre was started and had a major scene in Florida in the late '80s and early '90s, many of the best death metal bands come from Sweden. Check out Bloodbath and Amon Amarth, though I first got into death metal by listening to Behemoth.
Goth metal. Start with Lacuna Coil.
Groove metal. Start with Pantera. A no brainer.
Metalcore. Whatever you do, avoid my brother's band. Try Killswitch Engage, Shadows Fall, and Bullet For My Valentine.
Progressive metal. Many progressive metal bands sound COMPLETELY different from each other. I'm sure you're already familiar with Tool and I will get to Opeth in a sec.
Click here for more on Prog metal.
Thrash. Start with some of Metallica's early releases. New to Slayer? Start with
Christ Illusion.
Opeth. They're often labeled progressive death metal, but they really are their own genre. They do the heavy guitars and death growls, but clean vocals and acoustic sections are also important elements in many of their songs. Death metal bands normally don't do clean vocals. If you're REALLY into the heavy stuff, start with
Blackwater Park. Otherwise I suggest you start with
Watershed.
This post is just a basic walkthrough.