High-Res Logo Re-creation

I have a low-resolution copy of my logo and need it rebuilt from the ground up as a crisp, fully scalable vector. The main reason is future-proofing: I want to be able to open, tweak, recolour, and resize the artwork in both CorelDRAW and Adobe Illustrator without any loss of quality... (Budget: ₹600 - ₹1500 INR, Jobs: Adobe Illustrator, CorelDRAW, Graphic Design, Illustrator, Logo Design, Photoshop, Vector Design, Vector Tracing)