Choosing fabric for Bra Making is a little different than choosing fabrics for garment sewing. Cup fabrics and front frames are typically a low/no stretch, while the back band and in some bralettes and some sports bras, even the front frame is stretch. There's many people who have discussed this well, so I will share links of the favorites that I learned from when I began sewing bras.

Cloth Habit has a beautifully done page on the materials necessary.  

Click the pictures to read their post.

(pictures via cloth habit's website) 

Bra Makers supply is one of the more well known places to buy fabrics and attend classes. I've traveled to their store, taken in house and online classes and I love their kits. Click below on the supply list to see their explanation of fabrics.

Emerald Erin's videos are nice and clear & she shows the fabrics off.