I want to buy a distortion pedal and a wah pedal for my guitar, what should I get?
My budget is around 200-300 euro's, which is about 270-405 USD.
I really like the sound of Soundgarden (first albums) and Alice in Chains, should I just get a Boss DS-2 and a Dunlop Cry Baby?
I currently use an OLP McSwain Tin Top and a Roland Cube 30.

It would also be nice if I could use these pedals with a bass guitar, and perhaps the distortion for a drumcomputer, is that possible without raping the sound to much?

yes that combination is indeed a good choice... if you have some spare money get a better wah than crybaby 95 but the DS2 is awsum. and i dont think it would work with bass.. not sure
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Crybabys or Morley wah is good, though each wah usually has different tone characteristics. As for distortion, you should probably go to a music shop and play through a few pedals to find which tone you like best. The Boss DS-2 might be good, but you never know.
Boss distortions don't have much life... unless you want to do something really noisy and weird and get a Super Feedbacker, but those are hard to find. A Big Muff is always nice for grungey sort of work, too.