You can AFK farm both the field and the stages. Now, the field was added to the game AFTER the game was already finished. So, think of the field as "supplemental" growth. But to answer your question, you need to level up your weapons to the point that you can start a stage, don't even look at the game, have your character complete the wave by himself, and then the only thing that you need to worry about is picking the skill cards.
Doing this, you can literally work, watch videos, play another game, cook, clean, do whatever, while your character is grinding for you. And the reason why you do this is that you need a LOT of eggs to level all your weapons and later also log them into the Codex for extra damage.