I am/was an electrician before I went into the military (I’m still a member of I.B.E.W. Local 58). I would suggest running a 12 gauge wire from the hose to the chicken coop (unless you’re running other items besides basic lighting and plugs). Voltage drop starts to occur when you get around 220 or 250 feet. If you run a direct burial wire, I would suggest a 12/3 which means there is a black, red, white, and ground wire in it. The reason for this is so that you can put a switch in the house or garage to turn on a light at the coop. It’s just easier to turn on that light than to have to trek out to the coop at night if you hear something wrong out there.
It says you live in Capac. I can come out there and help you run it and show you what to do to hook everything up……just PM and I will give you my phone #. I live up in the North Branch area so it’s not a big deal to go out there.