In terms of leveling, repeating a quest like a royal audience is fastest. Just trash, so you can crank the difficulty way up. In terms of sanity maintenance; some areas of the game I vastly prefer to others... I tend to to repeat those over and over. (e.g. siege-breaker -> diablo) But that boils down to more personal preference.

Looting isn't so bad. set your viewers so that you can see your alt screens, and bind keys (I use F1-F4) to left click, that way after a champion/boss I just hit alt, loot the yellows on everyone and move on. It is time consuming, though. While leveling you can use the blacksmith in lieu of looting (e.g. if you are repeating a royal audience) to a degree.

Later on you might want to just ignore yellows in favor of checking the minimap and zone map for legendaries.