Hi Chris!
Definitely 410 or 416 Stainless for the cladding. Either is going to give you the best chances for success. I have also done some San-Mai with 316, and 304. It CAN be done with 316, but you have to fight it the entire way. For me 304 was a failure from the start.
These days I don't think there is a "good" source.
What I usually do is go to ebay and try to find a largish chunk of either 410 or 416 for a decent price, then I forge it to the sizes I need. Last time I found a 1 1/2" wide X 3/4" thick X 5' long "drop" and got it for $100 with shipping included. Forged out, that makes a bunch of 1/8" thick or less cladding material.