Cari's advice is really good.
I do a lot of machine embroidery and matching the fabric to the right stabilizer without making the fabric too stiff takes time to learn. If you are happy with the outcome of your practice square, I'd stick with that as you don't have enough time to do some test squares with all the different combinations possible. If this is just for a wall hanging the "feel" of the fabric is not so important so using a tearaway is fine.
I would suggest that you starch your fabric first. I use a spray starch that I get at the grocery store or "Best Press" that I get at quilt stores on thin fabrics like quilting cotton. I like Best Press best. It doesn't burn like regular starch. Starching makes it easier to machine embroider, but you may need to iron it after it comes out of the hoop.