OK, you need to make some assumptions here. If the blocks pictured are 16" finished, then I would 'guess' that the sashing strips are 2" finished, and the 2 borders are 6" finished, and you don't want to piece them.
This would make the pieced squares in the corners 6" finished. Sound about right?
So a swag estimate for the Gold borders would be 108" (length) minus the 2 squares (-12") or 96". This works out to 2 2/3 yards. I'd buy 3 to be on the safe side. (well if I liked the fabric, I'd buy 5 but that's a whole 'nuther story).
The red border would be 96 -12 = 84", or 2 1/3 yards, I'd get at least 2.5
Beige inner border & sashing 84 -12 = 72" exactly 2 yards. I'd get at least 2 1/2
Peach border, 31 pieces @ 16 1/5" 2.5" You should be able to get 16 pieces from 1 width, so 2 widths, you would need 1 yard.
ETA: I would also take a picture of the pattern with you to the quilt shop. They can reclaculate and verify the yardage.