Stick welders don't need to control gas flow, but some tig torches have a valve on them if you go that route.
Audio cable is typically easier to find as well, and it's often more flexible. As for high current diodes, check on ebay. You can sometimes grab them there for under $1 each and they can handle in excess of 300 amps. I have a few still here that I keep as spares.
The typical ford 130 amp is one of the most popular for this, but I forget the part number and typical application. If you simply google Ford 3G welder you'll find all the info you need.