Hiya. ^___^ I'd love to cosplay Kohaku, but it's just not me... so...here's my ideas...
Unless you are very, very neat about it, painting on fabric tends to look crummy... But one thing to point out is that you probably don't need to follow the exact pattern of the designs, as long as it looks relativley similar and nicely done... I'd recommend finding a nice stencil at a craft or fabric store for the shoulder design.
You can find very nice lace if you look around (I noticed Hobby Lobby had very nice lace for very cheap while I was there yesterday). Make sure to look at bridal lace as well, as it tends to be similar to anime lace.
As for the fabric, I'm not too knowledgeable about that, as I tend to use some nice slightly shiny, very stretchy heavy cotton that my Hancock's stocks for just about everything I make. But that wouldn't do at all for Kohaku, so I'd recommend making it from either a very nice silky fabric or rayon?? as long as you sew it very neatly, as it is another fabric that doesn't tend to be very forgiving.
Thought on the wig... get a shoulder length wavy wig and style it into two ponytails on either side right above where your ear would be, then cut one off about two or three inches from your head to make the hairstyle... I can help if you don't understand that. ^__^