Actually, if you're going historically-accurate from a Turkish standpoint, you may want to think about linen. It has some texture like you want, but it's lighter and more comfortable, and often times quite a bit cheaper than wool.
I do recommend fabrics-store.com for linen, and if you need something heavier for a cloak their heavyweight linen is fabulous, I use it for hakama. But if you want to know what it looks like and feels like, Joanns and Hancock do have linens. Just make sure the bolt says linen, not polyester or rayon linen-look. That's much different!
Founder and Vice-President, Madison Area Costuming Society, a chapter of the International Costumer's Guild
Strange Land Costuming - www.strangelandcostumes.com
Director, SF&F Masquerade
- COSTUMECON34 - Madison, Wisconsin - May 6-9, 2016 - www.costumecon34.com