No more than 1/8. Since you will be pounding it out and brazing it together, all the hammer dings and surface wobbles may not file out if you use thinner stock. Unless you're really good.
The thicker you make it, the more you have to take off at the end, so use your judgement. If you're pretty good with a forge/torch and a hammer, you could get away with 3/32.
Tom