The props you unlock refer to the color matching of the characters. After telling you a faster way to unlock props, enter the two-person battle mode, select the character you need in 3V3 mode and brush 10 turn (restart 10 times in a row) to generate a second suit (single character).
Billy needs the first three sets of S-assessments.
White Saiki needs to complete 40 tasks, and the task is in the upper left corner.
If you are homemade, you can use DLC to unlock all the characters, including two hidden characters and a special flame Ba Shen.