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Which type of wire do you use when connecting pots, switches, ground, etc. ...and why?
Solid copper, Stranded copper, stranded tinned copper, or other?

I like stranded, pre-tinned, copper. But thats partly because its readily available. Stranded copper would work just as well.

stranded, but I tin it myself (so I voted for plain-ol-stranded)

Stranded, I tin it myself. It's very easy to work with and stranded wire is efficiently better than solid. There's more surface area for signal to pass over. Yeah, probably doesn't matter much for the low level signals in guitar circuits but have you ever tried to wire a guitar with solid copper? PITA!!

Here;s a valid question.... What gauges do you use?

22-24 gauge. Pretty standard.