Stay away from wooden barrels. They do work OK, but only for a little while.
LOL.
Stainless has a higher coefficient of thermal expansion than mild steel, so it can warp faster.
Stainless is only truly stainless when passive. Once activated, it will still rust (heat will activate it).
If you're considering stainless, you'll want a low carbon alloy, like 304L, or 316L. Either would work better than 304 or 316.
316Ti would be great, but that's hard to come by, and very expensive.
Will it eventually rust. Yes. Will it outlast mild steel (of the same thickness). Yes. Just think about how much longer a stainless muffler lasts.