Hi, Terra. Welcome to the forum, glad you joined. And thanks for including your location, that helps.
Instead of giving you a square foot number for space I suggest you follow the link in my signature below about space for chickens. You'll see why I don't necessarily believe in those kinds of numbers. They are usually not a bad starting point but we are all unique. For some of us it's overkill, for some maybe not enough. You might see something in that article that will cause you to think about it a bit.
Whether you are in Murray, famous Harlan County, or Henderson you should have weather where your chickens can get outside into the run practically every day of the year. That takes some pressure off of your coop space as long as you manage them in a way that they can get to the run. If you will integrate more chickens or replacement chickens in the future or let a broody hen hatch chicks more room might come in handy. I know the price of building materials is sky high right now, you don't want to overbuild. If you build your run so it is predator proof you can leave your pop door open all the time which takes pressure off of your coop space. I'm a proponent of giving them all the room you reasonably can but you have to be reasonable.
If you are buying all the materials new, most less expensive dimensions of building materials come in 4' or 8' dimensions. You can usually save cutting and waste if you build to those dimensions. A 6' width isn't that bad, you may be able to use the cut-offs for nests or other things. Since your roof needs to slope so water doesn't stand that lets you use cheaper materials for the roof an maybe still have an overhang. Make sure the roof slopes away from doors so you don't get soaked going in and out when it rains.
For 10 chickens I'd want a walk-in coop. You need to be able to get to every location in that coop for many different reasons. With 10 chickens it's hard to build a reach-in coop where you can reach everywhere. Build it tall enough so you can stand up in it and enough room so you can work.
A 6' x 8' coop is probably not a bad size for you unless you see something in my article that jumps out at you to say smaller or larger. Other than cost, I never see anyone complaining about building it too big but some run into issues if it is to small.
I don't know how you plan to build your run. Your run is part of your "space system". My suggestion is to look at the size of the materials you are building it with. If it is mostly posts and wire you may be able to build it bigger for not a lot of cost. If it has a lot of lumber and roofing materials in it then it may get pretty expensive to make it bigger.
Good luck, and once again
