In another thread someone talked about getting guaranteed rares or better when finishing certain campaign modules for the first time. But I just finished Into the Black Forest for the first time, got a golden chest, but nothing was better than uncommon. (I also got a golden chest from Attack of the War Monkeys which gave me an Epic, but that was luck.)
The last time this was asked, I summarized it like so: HOWEVER, I'm no longer so sure about the statement "Subsequent times, there is no guaranteed minimum at all." I can't remember if I've been getting piles of Common-only loot. Since you are only guaranteed Uncommon-or-better the first time, and the chest is colored gold, there is possible confusion with the gold-colored multiplayer rewards (which guarantee Rare-or-better).
I can answer this: Raid on Ommlet: guaranteed Pickled Herring Kobold Encampment: once got an uncommon, the rest commons Tunnels into Darkness: about 50/50 common and uncommon White Skull Canyon: mostly commons, occasional uncommons and rares Wizard's Workshop and beyond, you seem to be guaranteed at least an uncommon in the final chest, even when repeating. This is also where the club rewards begin.