High-Res Logo Cleanup & Vectorization

I have 1–3 company logos saved only as JPEGs. Each needs the background completely removed so I can place them on any colour without a halo or stray pixels. After that, please supply the cleaned artwork in high-resolution transparent PNG for immediate web use and, if possible, rebuild each logo as a true vector (AI, EPS or SVG) so it scales perfectly for large-format print jobs as well.

Sharp edges, faithful colours and identical proportions to the originals are essential. A quick turnaround is appreciated, and feel free to use whatever you prefer—Photoshop, Illustrator or another vector tool—so long as the final files meet the quality needed for both online graphics and print materials.