I would like to use my logo across numerous marketing mediums ( website, brochures, flyers, etc.). What file formats should I request?

Vector file format will work for every mediums. After you selected a design you can get the vector files via designcrowd.

hi,
i submitted my design.I hope it meet your requirements .however if further changes require please do not hesitate to contact me .all the formats you mentioned can be provided.waiting for your earliest response.
regards .
canvasart