I second the wig idea. Check out CosWorx or Amphigory. In order to get your hair white you would have to bleach it several times (and even so, you might end up with frizzy, fried yellow hair). And this process can be expensive as I'm assuming you would want to have it done by a professional. A good wig is only going to cost you about $30.
What version of Ginko are you going to be doing? (Winter or summer) I'm looking at my DVDs right now and he's got several different items of clothing. Like zomgmissy said, look in your local thrift stores for clothes that you could modify or use. Or even better, sew them. For Ginko, I would stick with natural fibres such as cotton blends and linen.
However, since his clothes are 'Western' style and relatively plain looking, I think you should go the extra step to make your cosplay not only identifiable, but outstanding. Ginko carries around that box with him and it contains many different items that are a part of his profession as a Mushi-Shi. Make a scroll and paint pictures of Mushi on it that appear in the series. Make packets of medicine or other such things that Ginko collects or encounters along the way. Buy or make a fake cigarette (or whatever you want to call it.)
What would be really awesome is if you could get green contacts and style your wig in such a way where your right eye is always covered.
I would recommend that you watch the anime/ read the manga again and just take note of what Ginko does and his general personality. Then get plenty of reference pictures and just study them.
Good luck with the cosplay!
Edit: By the way, are you male or female? If you're female I would recommend that you bind and look into using make-up to make you look more masculine. If you're male, you might just want to look into a bit of make-up just to make your skin look more 'flawless' for photos.