Copper and tin, yes. Tin because it's lightweight, Copper because someday we may have electricity, but Bronze together because it's gonna be good for a decent while.
Honestly, I'm fine with just re-rolling every time, though I would think most of the fellows would have high-ish curiosity/military/diplomacy, and low faith/luck. Perhaps we can say that one of the stats will stay the same with each change, due to the influence of the previous Doge's policy?