This project is a great idea for a wedding present! It's also fun to make for yourself. I made it as part of my dinning room makeover.
I made this wall hanging out of items I already had. The base is cardboard from a cracker box. I cut out two piece of batting and hot glued them to it. Then I used a piece of material I cut up from an old throw pillow. I used my embroidery machine to embroider our last name, and year we were married.
Then I wrapped the material around the cardboard and hot glued it together.
I added some ribbon for detail, and also a faux pearl button. The main reason I added the ribbon was because I glued the material on a little uneven, I think it's less noticeable with the ribbon.
If you are giving this as a gift I would cover the back with material also.
If you don't have an embroidery machine you can probably use the same method with freezer stenciling. I would use a cotton material if you choose that route. Check it out Here. The options are endless. You could try different textures, add ruffles, or whatever you like!