Build it as big as you can manage. That will allow for giving the chickens more space (which is always better, and simplifies cleaning chores and air quality and wintertime and things like that) and/or adding more chickens in the future and/or using some of the bldg for storage.
Things built in the style of storage sheds work fine but ideally should have a lot more roof overhang than storage sheds usually have. Alternatively you can build a more traditionally chicken-coop-shaped thing, i.e. shed-roofed. Or, really, anything else, those are just the commonest options.
You want VERY LARGE openings in all the walls for lots and lots of airflow since you get hot summers. These could be openable house-style windows, but could alternatively just be very large expanses of wall where the plywood lifts off to reveal just hardware cloth (=galvanized 1/2" welded wire mesh), but you can replace the plywood panel for bad weather or wintertime. You will need at least one or two windows that, when closed, are still transparent for light.
10 chickens will need 8-10 linear feet of roost space. Also 3 nestboxes, whcih should be mounted so that they are distinctly LOWER THAN the roost, and need to have a steeply sloped lid or other arrangement to keep them from being roosted on and pooed into.
And, obviously, a feeder and waterer and a chicken-sized door so they can access the outdoors. For the outdoors, it is a real good idea to have a strongly built secure run even if the idea is for the chickens to free-range -- there WILL be times you want to confine them (e.g. when loose dogs are in the neighborhood, or you don't wnat them pooing all over the big fourth of july picnic) and it is awful nice not to have to lock them *indoors* then.
If you browse the coop design pages on this site (link near very top of page) you can get some ideas of what might work for you
Good luck, have fun,
Pat