Mats: jute and cork mats are all the rage these days. Ideal is not too thick (definitely not a workout mat) and not slippery (and yet increasing grip strength is good!).
Blocks: 4″ is the standard size, 3″ can be great for additional variations and use. Options for the material are foam, cork and wood (bamboo too) changes the weight of the blocks and the responsiveness of the block.
Blankets: the mexican blankets are standard because they are not too big and easily make all the shapes we ask of them to support our practice.
Strap: I’ve become a bigger fan of the quick release yoga strap, you can easily change the length and also buckle and unbuckle.
Balls: ballwork comes in particularly helpful with the feet and hands, although ballwork can be useful for every part of the body. A tennis ball size or smaller works well, with a similar firmness. See the two sellers below for balls intended specifically for body awareness.
Atlas of Anatomy by Thieme (Second Edition or comparable)
Anatomy & Yoga by Ellen Saltonstall
Yoga Anatomy by Leslie Kaminoff & Amy Matthews (Second Edition)
Ellen Saltonstall is a local NYC based Ansusara yoga teacher who has done this type of work for a very long time and sells balls of different sizes, textures and more. Her books are there as well.
Tune Up Fitness‘s line of Therapy Balls provide targeted self-massage trigger point therapy and help penetrate through layers of skin and muscle. It’s worth checking out as well.