Here's what to wear in the event you were wondering about the correct underpinnings for a gymnasium suit. This combination garment is a close relative of men's union suits. No fabric recommendations are given, but the pattern does specifically call for some knitted fabric (like that for men's undershirts) for the back waistband. Otherwise, cotton broadcloth or lawn are likely choices.
When not participating in sports, women at this period had an almost bewildering variety of undergarments to choose from, including corset covers, (no longer necessarily worn over corsets) brassieres, which seem to be identical to close-fitting corset covers, camisoles, chemises, step-in or envelope chemises, drawers, bloomers, and petticoats.