See that you've gotten some great answers...good luck with your project.
I like felt for framed projects and also fabrics that i have fused a backing on. usually use iron on interfacing. I hoop the interfacing lay the fabric on top and fuse the fabric right in the hoop with an iron. I discovered this method with my toilet paper covers and it really works well. Good luck! Kay
Use 100%cotton for wallhangings and quilt it together with a pellon (usally this is about 1/4 inch thick). If you have to use poly-cotton, be aware that it may be 'see-through' if overlapping any patchwork sections.
With either you can use any type of fabric/stabilizer. But if I'm quilting, I use 100% cotton. My stabilizer is med. wt for embroidery, unless it calls for a thinner stabilizer. Framed embroideries, you can use any type of fabric, because it is going in a frame which gives it support. A hanging needs more stability. I imagine you can do a wall hanging with any type of fabric, I'm just more into quilting...