For the Brotherhood robe, I'd say use Hopsack Linen or any linen look. It's cheap, but still a really nice feel and look to it. And, IMO, more true to the time period. But I'm totally biased on this. I'm using a linen look for AC2 costume. I don't remember what exactly the red lining fabric that I bought was. I just know it was a suiting fabric and it feels so nice and it's easy to work with so far.
The key for the money issue is to buy when it's on sale. If you're shopping Joann's, wait till it's 50% off and buy as much as you need. ^_^