The only uncommon champ that sees any regular use is Armiger. That said, you'll get a million of them from summons or from the market, so I wouldn't necessarily save them until you decide if you need them.

I'm not sure what you mean by "harvest food" - do you mean rank them up so you can feed them to higher-ranked champs to upgrade their ranks?

If so, there's basically two ways:

1. The easier of them is to just farm campaign 12-3 (or 12-6 if your farmer's affinity is bad for 12-3). Usually you'd want to target Brutal. If you haven't reached that level of progression yet, farm the one you can. Don't waste time farming other stages (for food).
2. Later in the game, when you get the right champs, you can farm food in dungeons. Personally, I use Bad-El Kazer for Dragon 20, and Akoth the Seared for Spider 20 and Ice Golem 20. I run them with those aforementioned champs, along with four food to level. It lets me farm both items and experience at the same time. But it does require you to have specific champs, and pretty good items.

Lastly - I'm not sure what you mean by "chests". Do you mean items in the chest slot? They should show up when you select the "Champions" button (to the left of the "BATTLE" button), and then select any of your inventory slots.

Or do you mean chests from Clan Boss? In which case, the contents of them go to their respective place - items in the aforementioned inventory screen, brews in the Tavern, and silver into your silver stash (visible at the top of the main screen).