Create Transparent Background for Logo

I have a single PNG file that I use as a website logo, but it still carries its original background. I need the image cleaned up so the unwanted areas become transparent and the logo can sit neatly on any page color. I’m flexible about which portions should stay opaque—if you see a more polished way to isolate the mark, feel free to propose it.

Please deliver the final artwork as a high-resolution PNG with true transparency preserved (and an editable layered file if you work in Photoshop or Illustrator). Accuracy of the cut-out and a crisp edge around the logo are the key acceptance criteria. A quick turnaround would be ideal so I can update the site promptly.