Convert Logo to High-Resolution

I already have my logo in a single JPEG file, but it falls apart when I try to print it. I need it rebuilt at a clean 300 DPI so it looks razor-sharp across all media. While I don’t want the concept changed, I would like subtle enhancements only—think crisper lines, balanced colours and perfect edge definition—so the final artwork feels polished rather than redesigned.

Here’s what I expect as the finished package:
• A master vector file (AI or SVG) and a high-resolution 300 DPI PNG with transparent background
• The refreshed artwork matching the current design faithfully, just refined for clarity
• Colour profile set for both print (CMYK) and screen (RGB) use

Please keep the workflow simple: take the existing JPEG, recreate it cleanly, apply those light enhancements and supply the final files ready for print, web and any future scaling needs.