It's probably best not to get specific instructions. They constrain you too much.

The cheapest way to build a chicken coop is to go to the local rubbish tip, or tip shop if the top doesn't let you fossick. Be a little imaginative with your design. For example, you can build them out of PVC water pipes. They are light, don't rot, wire can be pop riveted to them, and they are very easy to glue.

I also turned a 80 litre rubbish bin into a chicken feeder. Getting the design reliable was a few of weekends work of trail and error. However once done my time was paid back over and over again. A rubbish bin can hold an entire 30kg bad of food. It takes my chickens 3 months to go through a bag, so the reduces feeding to once per month. (We also gave then table scraps, which is a daily chore.) I also built a automatic water station out of an old office bin and a toilet inlet valve. The net result of all that is the chickens can got for months without you touching them, which is far longer than any family holiday.

Like some others here, I don't quite get the cost aspect. A carton of 12 eggs in about $6 here, and 3 chickens produce about 2 cartons a week. The food costs about $10/month. If you have a yard, food costs can be reduced by about 1/2 allowing them out during the day. Allowing them to graze can automated too - you just need a 12v electric car window opener connected to a battery, solar cell and timer. Again, if you get these things second hand they will cost you less than the $60 of food they save in a year.

All that said, yes it will take a few years to repay the costs, and even if you automate to the degree I did taking the table scraps out to them and getting the eggs remains a daily chore. To me the engineering project of "how can I automate this at least cost" was as interesting as the chickens themselves.