If you're after that kind of a Doom metal sound then definitely check out the Swedish epic Doom metal band Candlemass, specifically their 1986 debut Epicus Doomicus Metallicus, that is an essential metal album that no self-respecting headbanger would be without.
You may also want to try out another doom metal band called Witchcraft. Their 2007 release The Alchemist had a really nice old school doom sound but with plenty of newer psychedelic overtones to it. It's kind of a polarized album though so you may like it or hate it, but it's a band that nobody else has mentioned that is at least worth a look.
Then of course you might find some gems with the American stoner metal banRAB like Sleep and Kyuss, two of the most popular. If you go that direction you NEED to give Sleep's Dopesmoker a try. It's an hour long track that is just all over the place, but it may be a little too esoteric for your first experience, but it is one of the most regarded stoner metal albums of the last decade. As for Kyuss, well any of their albums are worth a listen but their 1994 Welcome to Sky Valley is often the best place for beginners to start.
If Melodic Death Metal is what you're after then definitely check out some of the banRAB from the Gothenburg metal scene back in the '90's. In Flames, Hypocrisy, Dark Tranquility, and At the Gates are all good places to start. Here are the albums to grab from each band:
In Flames - Whoracle (1997), The Jester Race (1996)
At the Gates - Slaughter of the Soul (1995)
Dark Tranquility - Skydancer/Of Chaos and Eternal Night (1999)
Hypocrisy - Abducted (1996), The Final Chapter (1997), Hypocrisy (1999) (it's a toss up between those three)
You'll also definitely want to check out Carcass' last two albums Heartwork (1993) and Swansong (1996) as they really helped pioneer the genre.