It depends on what you are farming for.  You are always farming.

For XP: Campaign, The highest area you can clear, except for the boss rounds.

If you have cleared Normal, then 12-6 normal is best until you open 11-6 in Hard,  Same between hard and brutal

Silver: Campaign, The highest area you can clear X-3,  the shields sell for more than other items.

Items:  Campaign, the appropriate area for that item.  Each area has a specific set, each level a specific piece.
If you are looking for endgame gear, go to the dungeons: that's where you will find the Epic 5* gear, but the RNG is much higher.  Start by farming Campaign for a basic set.

Champs:  Campaign again.  There's a few Champs you can farm,  they will appear in the Zone selection for each Area.

Upgrade items: Dungeons.  Minotaur's dungeon gives scrolls for masteries.  The potion dungeons give the potions to ascend your champs. 

Best Champ:
Any Champ with an AOE attack and/or counterattack.
All the starters have an AOE so can farm fairly well.  Executioner is talked about often and can be farmed.
As long as they can solo the level anyone can farm, dragging food along with them. 

Forming teams for Dungeons and Clan Battles is the point of the game.  The spider needs AOE,  Fire Knight needs multihit, etc.  Play with your teams and see what works.

There's a lot of abbreviations that I don't know. Can someone tell me what 12-6 is and AOE?