If you plan to distress it yourself, find out what the item is made of before you buy it. Costume grade synthetic materials don't take weathering the same as natural fibers.
For the tunic, you might get a better result by matching the fabric more closely. If you look for a cotton or cotton/linen garment you can either buy in white and use RIT dye to get a washed out black, or buy black and use dye remover to wash it out. I'd dye rather than strip, because the dye remover weakens the fabric and thread differently and because some black dyes fade to green rather than gray. Dye also tends to pool in folds and seams, which will give you a better washed out look.
The base garment looks like a kurta or kameez with a banded collar. If you shop around, you might be able to find one for a decent price in a better fabric than the costumes. I'd be surprised if you find one with the sleeves sewn on the same way as the one above, but you'll have the same issue with the costume piece.
If worse comes to worst, you might be able to get two button-down dress shirts with banded collars, make a straight cut across one of them from armpit to armpit and sew the bottom part onto the bottom of the other shirt at the waistline where the sash will cover the stitch. Pop off the buttons, and then stitch the seam the buttons were on over the buttonhole side up from your waistline to just high enough to get your head through easily.
EDIT: Hey, Amazon has a white cotton kurta pajama for ~$40.