I actually disagree with most of the recommendations so far.
In my view the best route into extreme metal is to trace it's evolution from further back, and this means exploring THRASH, and exploring it properly.
This may just be how it was for me, but I doubt it - listening to all these "entry" bands like In Flames and Soilwork is quite a wasted effort really, because eventually, even if you enjoy some of these recommendations, you will probably want to move onto other things, and you will have no idea where it all came from.
Certainly in my case, I spent quite a lot of time wandering from band to band (not uncommonly recommended here in fact), enjoying what I was listening to but also reaching the point where I wanted to check out a wider and wider range, and at that point I realised I had next to no grasp of the foundations of extreme metal.
For that reason I completely changed tack and dived into thrash metal - a huge genre which spans far beyond Metallica, Slayer and so on, and which in itself, I might add, can satisfy much of your desires for extremity and brutality on its own.
At this point it is so, SO much better when you come to explore early death metal and black metal. You have a greater appreciation of the forms involved, and you can appreciate those bands within the evolution of metal, rather than just scooping out a few names - completely out of context - based on recommendations.
This may sound long-winded, but it is so worth it, and I wish this message could be got across to more people taking their first steps into "extreme" metal.
As for recommendations, it would be a good idea to start off with some of the staples of the classic thrash sound, like Bonded By Blood by Exodus. There will be plenty to connect with easily on this album, and also signposts to more extreme releases.
After that, I think an album like Kreator's Pleasure to Kill is an excellent route into fast, dark, aggressive, influential thrash. It certainly had a big impact on me.
Possessed's Seven Churches is pretty much the textbook starting point when exploring the seeds of chaotic death metal (along with early Slayer of course), and checking out some early Sodom (and Bathory) will set you up nicely for checking out black metal acts if you chose to.
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Seriously though, I really feel strongly about this point. It is a false economy to just drift into vague recommendations like "Soilwork" or whatever, because while you may find you like many of these groups, it's not really getting you very far, and if you do reach the point where you want to explore 'underground' metal more thoroughly, you will not be able to rewardingly do so without a grounding in the myriad thrash releases that paved the way for today's genres.
Not to mention that this field holds a large bulk of the releases that still constitute pretty much the unsurpassed classics of extreme metal.
