A mat helps give some cushion to the floor and helps your feet feel grounded. A carpeted floor gives enough cushion, but sometimes your feet or hands slip. When you are choosing your mat, decide if you want a standard thickness or something more padded. If you work on a carpeted surface the standard 1/4" is fine. If you are on a hard surface, the extra padding is nice. Another feature is whether the mat is really "sticky." Most mats are fine but if you know you need the most sticky mat, look for the brand Tapas. It has the best "stickiness" properties of any brand we have used.
Blocks are useful for raising the floor when you are still building flexibility. They can be used for proper alignment or some supportive poses. You can choose from the fat or skinny blocks. If you don't know which to choose, the fat blocks are more useful for beginners.
A strap is used for building flexibility when stretching hamstrings and shoulders. A buckle or D-ring is nice to have on the strap so it can become a firm ring shape.
Bolsters are wonderful for restorative poses or supportive poses. These are large and difficult to carry back and forth to class. Having one at home or at the studio for your use is a nice advantage.
The foam wedge is one of our favorite props. It raises your hips to make sitting cross-legged more comfortable and it relieves pressure on wrists in downdog pose.
Let us know if you need more help in choosing and using your props. We have a video in the studio you can check out to show you different options for using your props