bantybev has expressed the "Rule of 4 and 10". These number are a *minimum* recommendation but are not written in stone. The square footages were decided on by the "Board of Tags", a secretive group of international voices who where rubber boots and meet twice a year on the railroad track between Budapest, Hungary and Vienna, Austria approximately 100 yards down the track from the station in Vienna.
The square footage determined by these "rules" are a very good guideline to go by. The rules will, in most instances, keep you from overloading your coop and run. Attention should be given to both the coop and run areas to be sure there is a ratio that will work correctly. For instance, a coop 4x8 will supposedly handle 8 chickens...but if you only build a 4x8 run to go with it, well, the entire facility would only handle 3 chickens because of the limitations of the run.
More room is naturally always better. Some people keep chickens successfully with less space than this....many more people keep chickens successfully with *more* room than this. With you just starting out I would recommend you start out without a heavy density of chickens in your housing. This way you can observe how the housing handles what you have...it's far easier to add a chicken or two than it is to rehome a couple of chickens or to build a larger coop or run. Plus, to begin with, the less chickens...the less food, water, POOP, etc., that has to be dealt with...so you get to learn how to do things without suddenly have to deal with problems associated with overpopulation.
I say give yourself a little breathing room....and the birds, too.
A question...How many eggs do you need each week?
My choice would be probably 6-7 large fowl birds in your coop...your run will handle maximum capacity of your coop so the 6-7 birds should have a decent amount of run space.
Best wishes,
Ed