I have to disagree with this. I have several guitars with different woods and they all sound ridiculously different through distortion. My Les Paul, SG, and Strat (mahogany body) sound a lot thicker and have this huge bump in the mids and sustain really well, especially the two with set necks. I usually have to cut the lows and mids and boost the highs on my amp/eq and sometimes even cut the lows before the amp. My other two Strats and my Luke (alder bodies) have a tighter sound, but not exactly brighter. They just have less mids and lows so it's easier to get chimey clean tones and still get warm, thick distorted tones. My Ibanez RGs (basswood bodies) are snappy as hell and have a very tight bottom with a bump in the higher mids. These do great in music where the guitar needs to cut through a heavy mix. This makes chugging easier because there is less low end to muddy up the distorted tone. I usually crank the bass and mids on the amp and sometimes I'll have to back off the highs or place the microphones at an angle to tame some of the brightness. Plus, basswood bodies are super light!
Of course, you can rely on the electronics that have the opposite affect of the body woods to get you where you want tonally (bright EMGs on a Les Paul), or you can use electronics to further push you in the same direction (hot and bright DiMarzio Evolutions on an Ibanez RG).
If you're playing a lot of different styles, clean and dirty, and you want to use just one guitar, I'd recommend either a solid alder body or basswood body with a maple cap, a bolt on maple neck, fretboard of your choice (I like rosewood, birdseye maple, and ebony), stainless steel frets (trust me on this!), and a non-locking tremolo (or a locking tremolo without a recessed cavity). I also recommend a H/S/S configuration. You'll want pickups that aren't specific for one style or another so I'd go with something PAF-like in the bridge (DiMarzio AT-1, Fred, PAF Pro) and some fat single coil-sized humbuckers (to keep things quiet) in the the the other two positions. Maybe a couple of DiMarzio Cruisers (fat Strat sound), or a Chopper (higher output, more mids) in the neck, Cruiser in the middle.