The size of coop and run you are considering would work for 1 chicken, although the run could even be a bit larger.
Here are a few things to think about.
Are you going to keep your chickens locked up in the coop for longer than overnight? If so, you will need more than 4 sq. ft. of space per chicken.
The more room your chickens have, the less likely you will have problems with them picking feathers and drawing blood from each other.
The more space you have, the easier it will be to keep clean. Chickens produce a lot of poop, and if they are confined to a small area, it builds up quick.
If you are getting 5 or less chickens, I suggest your coop be at least 4X8.
I would put the run on the 8 foot side, and make it at least 8x8.
I would also make them both tall enough to walk into. You will appreciate the height later on, when you have a hen that decides to hide her eggs and not lay in the nest.
As you add more chickens, you can build another coop next to this one and just keep growing!!!
I don't know where you are, but if the weather is not too harsh there, someone on here made a hoop house from PVC pipe and covered it with wire , then a tarp.
https://www.backyardchickens.com/forum/viewtopic.php?id=29631
Here is a link to one that is not tall enough to walk into, but it will give you the idea.
http://4hpoultry.osu.edu/HoopHouse.htm
And here is one we made from a trampoline frame.
https://www.backyardchickens.com/forum/viewtopic.php?id=43233&p=1
Here are some breeder pens we built, and after using these for 3 years, I sure wish we had made them taller! There are other pics of pens in this thread also.
https://www.backyardchickens.com/forum/viewtopic.php?pid=395113#p395113
Hope these give you some ideas.
Jean