Vectorize and Refine Company Logo

I already have an logo that captures the spirit of my brand, but every free converter I try turns it blurry or pixelated. What I need now is a clean, professional vector version that preserves the original look while tightening the edges and fine-tuning the colours... (Budget: £20 - £250 GBP, Jobs: Adobe Illustrator, Graphic Design, Illustrator, Logo Animation, Logo Design, Photoshop, Print Design, SVG, Vector Design, Vectorization)