You can cover the plane using Sig Stix it or Balsarite. These are both glues that are painted on the areas of the plane that will contact the fabric. After the glue dries, the fabric is ironed on to the framework similar to monokote. The heat from the iron activates the glue which then allows the fabric to stick to the frame. After covering, the plane can be painted with a paint such as linear polyurethane or an exterior latex. Do a google search for Jerry Nelson paints for the linear polyurethane. The house paint is available at any hardware store.

I don't think cotton will shrink with heat so you will have to tighten it yourself while you are applying the fabric. A better substitute for the cotton is dacron or dress lining. These can be shrunk with heat.