Believe it or not, there are many types of fabrics that will work for slipcovering. The most common however are cotton denim and linen. Not only do both of these offer the quintessential slipcover look but also the practicalities of being able to be washed and dried. I have a source of a wonderful brushed bull denim so feel free to contact me about that!
Performance fabric are becoming increasingly popular and now there are a wide range to choose from. Some can be washed while others are spot clean only. Revolution Fabric, Sunbrella, and Crypton are just a few brands.
If you are looking for something lux, velvet is another option. Velvet is one of the most durable fabrics and often comes at a great price. If you decide to go down that road, choose a velvet with a little drape in it to get the best look.
Fabrics that are not a good option would be one with a very stiff backing or one that is too light weight. It is good to stick with 10 oz or heavier.
Local fabric stores I would recommend in the area are Cutting Corners and Childress. Both stores will be happy to help steer you in the right direction for finding great slipcover options! I am always happy to further discuss fabric with you so feel free to reach out!