Before you make a bed quilt with trapunto you might want to experiment with some sample "sandwiches" to decide how you want it to look.
Try different battings and different threads.
You will probably want to use a base batting (cotton or 80/20 blend?) with the trapuntoed areas filled with either wool or polyester. The density of your background quilting depends on the look you want and the battings you use, and the weight of the thread will effect the amount of stiffness in the finished product. The thinner the thread, the less stiff the result.
For instance, a background quilted with something like Superior's King Tut will be much stiffer than one quilted the same density with MasterPiece. Background fill with silk thread will be the most drape-able, but it's costly.
You can also quilt several lines of echo quilting around your trapunto motifs, but less dense for the rest of the fill.
Check out Karen McTavish's web site for some inspiration:
http://www.designerquilts.com/gallery.html
Her books are great sources of information about trapuntoed quilts:
http://www.designerquilts.com/products.html