Here's how to change the Start button if you haven't figured it out (longer method no longer required for Classic Shell 3.9.1 & later, see above):
To change the Start button from the default button to a custom button,
1. Open Start Menu settings by right clicking the button.
2. If only basic settings are showing, enable all settings.
3. Go to the 'Start Button' tab.
4. To set your own button, click "Custom Button".
5. Then click on 'Button Image' and then click again on the [...] button next to it.
6. Browse to the Start button image of your choice. The image should have 3 states - normal, hot (mouse hovered state) and pressed. The image must be a 32-bit PNG or BMP (24-bit BMP may not show properly as it doesn't support transparency).
7. Setting the width of the button is optional. 0 means it will use the width of the button image as the size. You can override that by entering a custom width to make the Start button smaller or larger.