I would use 4 inch squares for the HST's and then trim to size.
For the 16 patch squares I would sew 2 1/2" strips in sets of four then cut 2 1/2" pieces toss every thing together then sew into 16 patch blocks - should turn out pretty random. OR you could just sew 2 1/2" strips into sets of 8 - then sew into a tube like you would for a bargello. Cut into 2 1/2" tubes and pick out a seam at random then pick out the middle seam to get your random 4 patch strips. Again toss these together then pull out by 4's to sew into the 16 patch blocks.