Yes it is ok to quilt with polyester and piece with cotton. Many longarm Quilters use polyester thread- cotton tends to break easily with the high speed of the longarm machine. Superior Threads have some great ( free) charts and information to teach you about different threads, needles, when to use what and what needles work for what Threads. They are a great resource. Spend some time browsing their information and sign up for their newsletter and tutorials. You can learn a lot and they are great for troubleshooting too.
I piece a lot with polyester and even silk threads. You can quilt with invisible thread too. Superior threads carries a great Aurifil invisible thread that quilts up great, and holds up over time too.