Print-Ready Logo Vectorization

I need this company logo rebuilt as a true, fully-scalable vector so it can be used for high-quality screen printing on apparel. At the moment all I have is a JPEG, and the artwork is complex enough that an automated trace will not capture the detail or keep the edges crisp... (Budget: $10 - $30 USD, Jobs: Adobe Creative Cloud, Adobe Illustrator, Adobe Photoshop, Graphic Design, Illustrator, Logo Design, Photoshop, Print Design, Vector Tracing, Vectorization)