There's no difference in rarity, except that rares start at 3*, epics at 4*, and legos at 5*.

I know this may not be the most efficient way (energy wise, but time wise maybe so), but I open a ton of green shards, level 1/2 of the commons to 10 then use the other half to ascend them.  Then I level 1/3 of 2s to 20 and use the other uncommons to ascend them to 3s, and so on.  In the end, I have 5s commons (for the most part usually) to upgrade leggos and 5s epics.

Not the most efficent, but it is what I do.

My personal routine is:

1 NM + 1 normal run to level 1* food to level 10

4 NM + 1 normal run to level 2* food to level 20

21 NM (or maybe it was 22, I forget) + 1 hard run to level 3* food to level 30

4* food I usually put in the pit to level to 40. 5* champs I level to 57 through minotaur then finish off with brews usually.

Hmm, nothing like a golden recipe, then. Thanks.

Rank  up most common  to  2  to  feed  uncommon  then  largely  use  Uncommon  the  rest  of  the  way.  Was  going  to  start  eating  rares but now  having  2nd  thoughts.  Have  a  few  i  dont  need  for  gaurdian  circle  so  maybe  ill  do  it  carefully.  

I posted this a bit back. It is the math and how I generated some chickens. There were some comments that had someother options but I am still testing those out. This scenerio battle on 12-3 Brutal with one champ who can solo and the rest tag along to gain XP. I hope it helps:

Step 1: 3 x 2* participating in 10 battles @ 8 energy each generate 3x 20 lvl champs. This costs 80 energy. It generates 11k coins per battle and on avg a shield that you can sell for 9k so about 20k coins so over 10 battles that is 200k coins.

Step 2: 3 x champs then eat 6 x 2* champs to generate 3 x 3* champs. This costs 4k/champ so 12k for upgrade.

Step 3: 3 x 3* champs then require 24 battles to max at lvl 30. Costing 192 energy. Generating  480k coins.

Step 4: Requires you to complete steps 1 and 2 three more times. Costing 240 energy. Generating 564k coins.

Step 5. 3 x lvl 30 champs eat 9 lvl 1 3* champs. Costing 9600 coins per champ for 28,800 coins.

This means in total for 3 x lvl 4* champs it cost me 512 energy and generated about  1.2 million coins. My average run time per battle is about 25 seconds with Genbo so 64 battles at 25 seconds is about 27 minutes of game time.

An important note. These are averages and don't account for mystery shard generation or random drops
(mostly Incubus you will use to feed the grind, Hound Spawn into Faction Guardian slots). 

Yea, I do this similarly. Set the Big 'Un to farm fast, 9 sec, so it goes quite quickly. Problem is energy and the number of champions you feed.

Thought there is some better, more efficient way, but... guess not.

When you hit end game and get lucky enough to pull the right champion, and have the correct gear of sufficient quality, you'll he able to level food in dungeons with one champion doing all the work. It is a lot slower per run of course, but you get to double dip experience and gear for the energy price of one. 

But it takes quite a while to be in a position to do this.