I hope this works! Here's a pic of your quilt with some quilting ideas on it. You could do an overall fill design in the beige blocks - that would really make your stars "pop." Or, if you used a flower-like design (as shown) in the center of the star, you could carry that design into the beige blocks.
For backing - that's totally your choice. Sometimes I choose a fabric that plays nicely with the front - same color scheme, for instance. Other times, I go with something radically different. In this case, I'd probably try to find something that had both beige and red in it - a toile would be nice.