Advanced players typically do the King’s fall raid Tuesday through Thursday and do trials of Osiris Friday through Monday, as well as Iron banner and other special events (ex: Crimson Doubles) whenever they’re out.
In King’s Fall, if you have multiple characters, take one group to totems, then everybody switches characters (leaving one man in raid while others switch). This will give each character a checkpoint where the good rewards begin.
Each week, King’s fall has different challenge for boss fights (Warpriest, Golgoroth, oryx) with specific rules for how to beat that specific boss. In normal mode, guaranteed 310 item. Each boss drops one of two (if not both) specific item slots i.e Oryx challenge drops helmet and or Primary, one of which is guaranteed 310, second if it falls is b/w 300 and 310. Hard mode 1 reward guaranteed 320. If second drops, b/w 310-320. For example, Warpriest drops several items, including the Defiance of Yasmine sniper rifle (there’s one legendary with higher aim assist, but it doesn’t compare with range and impact).