would recommend, from experience, a cheap shed rather than a coop.
better value for money, you can stand up it & its easier to clean (though if you are as tall as me, you can still regularly get a good crack on the head! saw stars twice last night, once going in and then again on the way out! )
obviously, this wouldnt be moveable, but could eg be a winter house with room for storage.
if youre prepared to wait, you could get a second hand one from eg gumtree, preloved, e-bay or your local paper...