I live in Australia in the dry tropics of the NT.
I have a chookpen design that works, in the dry tropics, wet tropics and temperate region. It is very very successful.
Firstly, a garden that is 30' x 40' will produce countless vegetables on an annual basis. Use what you have.
Take a large area, and build your chookhouse in the middle of the area with a door either side........ string your dividing fence off that..Dont make it too elaborate, my chooks roost in an area that is 6'x6'. It's basically a manure collection point.
This makes one side for chooks the other side for vegies, what you grow is your choice but the chooks can clean up one side for a few months...... whilst you garden the other. Any trimmings or damaged stuff is tossed over fence to waiting chooks. One plant I would encourage any chicken/vegie gardener to grow is the herb Rocket. I dont like eating it much, but it makes the chickens lay. I have seen it make old battery hens start laying again.
Another very good plant that I let establish in the vegie garden side is pawpaw or papaya. By the time the vegies are done. The papaya is big enough to handle the chooks, it provides them nice shelter and again the pawpaw flowers seem to control internal parasites in the poultry. Chickens love pawpaws and pawpaw leaves. They cannot roost in pawpaw so that isnt a problem.
In temperate areas use pigeon pea in place of pawpaw. The sticks make great kindling, again they are a nitrogen fixer and can handle raw poultry manure. Pigeon pea was great, we prefer pawpaw. I normally let about a dozen or so establish.
Once you have one side cleaned up, about 6 months for me....... take the chooks out... put the water on for a couple of days........ and let any weed seeds germinate. Then, put the chooks back to clean them up for a few days. I chop the heads off the pawpaw and throw them to the chooks. The pawpaw posts can be used to grow things up and rot down very quickly anyway.
Using this system I have converted red tipra soils [very fine and rock hard clay] into lovely soil in a year. I dug the postholes with a crowbar when i started. Now I can drive the crowbar 18" by hand. Worms abound.
I rake the entire 'clean' area into a heap and leave it to compost for a few months.......... I throw all sorts into the chooks, prunings etc. and let them scratch them round. When i am about to use the compost, i hook the sticks out and either use them as row markers or have a little fire.
I then lay out my seeds, fairly thickly and use compost over the top of them. I also put hay over the top in a very 'light' manner. This forms a microclimate and protects tiny seedlings... eventually it flattens out...
My inputs into this apart from the obvious is some local grain and normally a big round bale of sorghum hay which i throw in the chook side. They kick the hay all over the yard, eat the grain and generally have a fine old time with it. I dont buy quality hay, usually rain damaged.
My estimated annual bill for chook food and hay is about usd 6 per month for grain and usd 10 per annum for hay.
One of the great advantages of this system are the 3 spare fences and the windbreak/shade they offer. I dont grow pumpkins in this setup due to space. I have lots outside, I live on 80 acres.
Out of 20-30 mixed fowl [we have that many because we like them] my kids make about usd 50 per annum out of egg & chicken sales. My wife makes much the same [she sells eggs at work]. I barter many of my vegies for meat, fish, expertise, some help around the place. I have costed in the hay, but only ever bought it once. Now my hay man arrives with his worst hay, sometimes 3 bales......... and he takes my best vegies.
The chook pen cost me about USD 50 to build.
My family is self sufficient in poultry, eggs............. and every vegetable thing but potatoes. I supply a single old man with his vegies......he eats so little. He supplies me with mangoes and assistance with my bore pump.
This system takes on average about 2 hours per week and that is a gross exaggeration. On many evenings a year my wife sits on her seat/rock with a glass of wine. Whilst I play gardening.
I don't know how people can garden without chooks!!
PS........ my builder, mechanic, solicitor and 2 of my kids teachers now have similar set ups..