Recreate & Vectorize Two Logos

I have two existing logos saved only as JPEGs that now need to be stitched onto apparel, so I must get them converted into clean, scalable vector artwork suitable for an embroidery machine. The basic look... (Budget: $250 - $750 USD, Jobs: Adobe Creative Cloud, Adobe Illustrator, Adobe Photoshop, Graphic Design, Illustrator, Logo Design, Photoshop, Vector Design)