I use sheets for backing and piecing and have machine and hand quilted them. I found quilting with my machine I had to use a denim needle- I think it was a 90/14. I was getting missed stitches, but after I switched needles I had no problems.
I use mostly vintage (thrift store) sheets, and try to use like fabric with like, such as 100% cotton with 100% cotton, etc. I also don't use the really high thread counts- the needle makes little "puck" noises when it goes through, so I think it is probably tearing threads.
In my mind, fabric is fabric. I cut up old clothes, too!