Check out Opeth. They have a wide variety of metal genres they use. Hell, they use a wide variety of a lot of different genres in their music (folk, acoustic, jazz, blues, rock, etc). I'd label them as progressive metal.
Most of their songs are 8-10 minutes long. Very epic, but very beautiful. It's much more about musicality than technicality. All of their music is written by Mikael Akerfeldt, and he is an incredible musician. His metal growl is one of the best I've heard, and he has a beautiful singing voice. His lyrics are extremely poetic, and the music he writes can be chillingly beautiful, brutal, fun, and/or weird. He's also one of the guitarists in the band. Basically, Opeth is a group of people that play the music Akerfeldt puts together.
I found that I had to listen to the first album I got from them about 5-10 times completely through before I "got it". I was a big metal fan already, so give them plenty of time to grow on you. I think out of all the metal bands I've had non-metal fans listen to, Opeth is most likely to impress.
Their first two albums ("Orchid" and "Morningrise") are more in the death metal genre. TBH, I've never been able to get into those two. Albums after that more closely represent the normal Opeth sound. I would recommend starting with "Ghost Reveries", as I feel it's their most polished album and gives you a good idea of everything Opeth does. The opening track on that album is my favorite song of theirs.
"Watershed" is their latest album (until their new one releases in September). It's quite a bit different from everything they've done before. It's more technical and has a much weirder vibe to it than their previous albums. Fantastic album, really. It's often under appreciated. Yeah, it doesn't sound like their older stuff, but Akerfeldt did not disappoint in his writing abilities.
In Flames is another metal band I'd highly recommend. To be more specific, I recommend you listen to "The Jester Race" through "Clayman". Their first album, "Lunar Strain", wasn't that great IMO. Their style dramatically changed after "Clayman". People don't realize this, but In Flames was a HUGE influence in metal. There are countless metal bands that credit them as an influence...and if they don't, they probably credit a band that credited In Flames.
With In Flames, they're all about melody. Sure, the vocalist is growling and hard to understand, and the guitars have plenty of distortion. But behind the "metal" is beautiful music. Their newer stuff sounds more generic, more whiny, and just doesn't sound as beautiful as it did before. I still like it and appreciate it, but early In Flames sound like music written by talented musicians. Their new stuff sounds like it's written by a group of younger kids.
I'd also recommend checking out Between the Buried and Me. I recommend their "Colors" album. They're a very technical, progressive metal band.
There is also Dream Theater. They're a progressive metal band. Their lead guitarist is incredible. No death metal growls or screaming to be found here.