I have been doing this for sixty years, off and on. You are right. People like a change when I haul out the harmonica and play a verse through the mic.
Bare in mind that you have to play in the same key as the harmonica, which brings us to the next question. I have about 15 of them in different keys and sizes and quality. They range in size from small Marine Band harps in different keys to large chromatic Super harmonicas.
I would start out with a small Hohner blues harp in "C", or a double sided C & G. Whereas the chromatics can play in the cracks, so to speak, they are much harder to master. Stick to a plain diatonic to start.
Bernie
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