Image Vectorisation for Logo

I have a raster image that I need converted into a clean, fully-scalable vector logo. The end use is branding, so the paths must be crisp, colours matched accurately, and shapes rebuilt—not simply auto-traced... (Budget: $10 - $30 USD, Jobs: Adobe Creative Cloud, Adobe Illustrator, Graphic Design, Illustrator, Logo Design, Photoshop, Vector Design, Vector Tracing)