I agree with the recommendation of using straw needles and Superior's Bottom Line thread. One of the great things about Bottom Line is you can purchase collections of colors, wound on bobbins and sold in bobbin rings. This makes it ideal for applique and EPP.
However, instead of using a whip stitch to sew your hexies together, I highly recommend using what's called the ladder stitch. I've used both, but disliked the fact that my whip stitches were visible. I found that using the ladder stitch solved this problem.
