This is what works for me.
In fall and spring I have alfalfa and brassicas. Summer soybean, garden extras like corn and tomato, and grass clippings. Winter, rye or wheat plants. 10 months a year bugs and worms.
Alfalfa. Has omegas that will make your eggs dark orange and taste great. Is also 30% protein, half that of steak. So it's like half steak and half veggies. Alfalfa will keep coming back for years too. Also for summer soybean plants, not seeds, are about the same. Chickens eat the leaves.
Kale. Lower protein but high in many vitamins. Any cheap brassica seeds you can plant. Again does well giving a late fall and early spring snack.
Wheat, rye. Plant in fall, will grow in coldest months and you can get them green stuff even in January. Whatever survives winter grazing will have heads on it following July. If your garden is dormant, might as well plant wheat in October and let chickens eat it until you plant the next spring.