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I use a super cheap Lafayette Mic that was made in the sixties, instant distorted low fi tones because it cannot handle much else LOL. I sometimes set up one regular mic and then the old one for distortion effects and go between the two as the song warrants. Bob Log III, a low fi one man blues band sings with a motorcycle helmet on which has an old phone built into it, freakin awesome sound and it looks crazy too! Tight white's suggestion will work too, even little old solid state amps can work, the Guy from the Strokes I think sang through and old peavey.
Good luck and let us know what you end up doing.