I think I would use Hobbs wool. This is a very well-known and tried-and-true batting. This batting is also very easy to hand quilt, which means it will also be easy to hand tie. (Wool is much easier to hand quilt than cotton.)
I would use embroidery thread for the ties, but I'm thinking you might want to have the ties on the underside of the quilt. Hobbs wool batting requires quilting lines 4" apart, so ties would need to be very close together. What you might want to do is stitch-in-the-ditch with a fine thread such as Invisafil to secure the quilt, then add ties or small quilting designs here and there within each block.
Have all the materials been pre-washed? I would also pre-wash the batting. Here is a link to information about the Hobbs wool:
http://www.hobbsbatting.com/products...washable-wool/