As a woman I feel one needs a variety of underwear and bras; especially if you are in the fine arts. If you do musicals you have a plethora of undergarments because there are so many needed for different dresses and dances. I feel these are the basics.
One should invest in:
tan character shoes
black character shoes
a nude one piece (leotard)
a supportive bra that you can dance in; mind you sports bras not allowed.
Those are the basics that I feel are needed. Some girls include spanks, corsets and body pieces. But I do not wear those items.
Other clothing I feel dancers and actors should have include leggings, tights, pairs upon pairs of shorts, jumpers, more leotards, head bands, required shoes and lots of tight dance shirts.