When using cotton fabrics always use a cotton or wool batting. If the quilt is going to need washing fairly often then for sure use cotton. Polyester batting will completely destroy cotton fabric in 20-30 years. Learned this in my quilt restoration workshops.
I would add a border around the whole quilt. It doesn't need to be a wide border just something to separate the blocks from the binding. Any color you think would look nice with the general look of the quilt a matching backing would be nice to use with the binding. What about quilting a circle in the space of four adjoining blocks, give it a little bit of curve so it has more movement than just angular lines. Use string and a chalk marker to make the circles or trace around something that fits inside the four blocks. Just an idea to kick around.