What is the recommended image size for the logo?

A bit off-topic, but that said, if you choose having large and heavy PNG logos, consider using a PNG optimizer like https://tinypng.com/ or https://pngquant.org/ (same thing, but as a desktop/command line app). Depending of your image, you can have a substantial decrease in your image weight, and the color loss due to the compression can be pretty much invisible to the human eyes.