I'm in the woods and I use autumn leaves both in the run and in the coop. I gather them via the lawnmower with a bagger on it so they're chopped up a bit. Dump them in the run and the coop. The chopped leaves begin to compost down in short order and attract the leaf-eating earth worms that the chickens love. I combine them with pine shavings as deep litter in the coop and the girls love it. When spring comes, I rake them up from the run and coop - with the addition of that wonderful chicken poo - and put them in my bin composter. They're mostly broken down at that point and make it to the garden in a few months when they've composted further.
I do not allow them to eat any foods from our actual household compost pile that includes rotting fruits, veggies, etc. I lost one bird last summer to what I'm pretty sure was botulism and eating from the household compost is a good way to make a bird sick, especially in high heat.
I grew marigolds last year for the girls. They HATED them. Wouldn't touch 'em. I ended up throwing the marigold heads into the coop and it brightened up the floor a bit! They ended up in the compost pile last fall and will hit the garden this spring.
I find that my girls love leafy greens so I grow extra lettuce, cabbage, kale and collards for them. I grow extra in the garden and I will also grow it in pots. Some of the lettuce and kale's are very pretty and look ornamental so they're nice to have on the deck. You can keep them from bolting early by planting them in an area that will be shaded when the trees leaf out. Their favorite veggie is definitely cucumber and I usually have so many of them that's it's no problem sharing.
When the garden is done in late fall, I let the girls in to clean up the bugs and weeds. Just now moving them out of the garden space as we get ready for spring planting. I sure hope they got all those blasted cucumber beetles!