Floor, "Find Away"
In some ways, there's some real similarities between My Bloody Valentine and Floor. Both use a ton of guitar to sometimes disorienting effect, but leaven them with vocals that are kind of at odds with the overall tone. MBV uses dream-like vocals, and Floor uses clean singing (which is unexpected in something this heavy), but it results in a dual thing that gives them a really interesting feel.
Fugazi, "Bad Mouth"
I was asked today for a recommendation for a first Fugazi album, and it's kind of a tough question. I think that their records present some different facets from each other, and so it depends a little on what you're looking for. I can make a good case for The Argument, In On The Kill Taker, End Hits, or today's record, 13 Songs. The argument for this record is that it's probably the most approachable Fugazi record, as there are a number of songs on it that are kind of...well, groovy. It's not something you encounter quite as often in their later records (although it's also not totally absent).
OutKast, "Skew It On The Bar-B"
Meanwhile, Aquemini is the correct OutKast record to start with.
Stubborn All-Stars, "True Mental"
This is from the third Stubborn All-Stars record, Nex Music, which is a very good time (although maybe not as good as the previous album). Like all the All-Stars records, it's helped quite a bit by having a strong roster of ska veterans like Vic Ruggiero and Agent Jay (both from the Slackers) helping things along. They tend to go more for the rocksteady end of things, even the occasional dub song, and if you like this, you should look up their albums.
Metallica combined metal and hardcore to give us thrash, and the first record really shows the hardcore contribution to their sound. This really isn't that far from hardcore at all, outside of the most flaming guitar moments.