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The biggest mistake most new chicken owners make, is not giving their chickens enough space, by buying a coop from the local feed store and assuming they are truthful in their advertising about how many chickens can live in it.
Most pre-fab coops the feed stores sell are cheaply-made, not predator-proof, don't last very long, and can only support about half the number of hens they claim.
It's definitely more cost-effective, safer, and more humane for your chickens to do your research on coops here and then build one yourself, or if your finances allow it, hire an experienced chicken-knowledgable person to build it. Or buy a pre-fab for two or three hens for now, with plans to expand it and surround it with a more secure yard as soon as you can.
The second-most common issue is the chickens' run becoming wet and muddy, they quickly destroy the grass and vegetation way faster than most people would expect. If you have only a few hens but a large area, you can solve this by housing them in a "chicken tractor" in other words a coop that is mobile (there are many designs for this you can find on here by doing a search) and moving it to a new area before the old area gets overgrazed and muddy. This is a great way to go if you also grow a garden - the chickens can do all your composting and rototilling for you, as well as fertilizing each area in turn.