Vectorize Logo for Print & Embroidery

I already have the design in PDF format and I’m happy with its overall look—I just need it rebuilt as a true vector so it can scale from tiny business-card size all the way up to an embroidery hoop without a single jagged pixel... (Budget: $10 - $30 USD, Jobs: Adobe Illustrator, Digital Art, Graphic Design, Illustration, Illustrator, Logo Design, Photoshop, Print Design, Vector Design, Vectorization)