Chickens like short grass and do poorly in tall grass. I can see this as I mow the pasture, because the chickens get excited about the foraging prospects of the newly mown swath, rushing around excitedly looking for bugs and yummy young plants revealed once the tall grass has been cut.
Grass has few calories but lots of vitamins and protein. Chickens can only digest grass if it’s young and it still bright green. Once it starts to fade, they lose interest.
Physically, tall grass is an impediment to them, preventing them from going where they want. It also triggers annoying behaviors like laying eggs in the grass rather than in the nest houses, and encouraging them to hunker down and hide rather than run when frightened, raising the possibility that they’ll allow the tractor to run them down. I’ve only ever killed one chicken with the mower. That was enough.
Back in the good old days, there was some research done along these lines, and mowing the grass down to two inches tested out as being optimum. Six inches was too high.
I’m a big fan of permanent pasture (never plow, never reseed), since it combines the minimum amount of work with the maximum amount of pasture-plant diversity. So I’m not up on which plants would be best if you were starting with a plowed field. In general, at this time of year you should plant a grass or clover that will stay green all summer and do well if mown down to two inches. In the fall, you want a grass that will stay green all winter and do well if equally short.