Hi Axel,
I'd go with a basic but decent quality vocal mic, like a Shure SM58 or equivalent. But instead of distorting the vocals while recording, I'd record clean, setting my levels so I don't go in the red, and shoot for capturing the best raw vocal performance I could.
Then I'd route that pristine vocal track thru any of the cool dirtying contraptions mentioned, and record that separately. Then I could experiment at will, comparing apples to apples, to find what works best.
When THEE DIRTYBEATS recorded its ep, we did something similar, in that we handled the processing of the vocals as an entirely separate step. We first recorded all the instruments live as a band, straight through, using a scratch track for the vocals, and later replaced the scratch track with more focused, better-recorded vocal performances. Vocal effects like overdrive, compression, and reverb were added after the fact, during mixing.
Hope this helps,
Andras
THEE DIRTYBEATS - 100% maximum vintage garage