Every color creates an emotional reaction for people, so be sure to consider those reactions when you select colors for your logo and your website. It all needs to work for you as you represent yourself, your business, or your group.
What emotion do you want to evoke with your website? Confidence, energy, caring? Then consider the condition of the people arriving at your website and how you want to use color to influence them.
If your website will help people going through a crisis then soft, calming colors would be a nice choice, like pastels.
If you are a fitness instructor and you want to get people off their couches, then high energy colors like vibrant Reds and Oranges would work.
Are you a contractor? Selecting the colors Red and Black will demonstrate the energy and power that you put into your jobs.
Is your group working to save the environment? Then I bet you can guess Green would be a good color.
If you want to exude confidence and reliability, then Blue is the color for you.
In addition to considering the color itself, be aware of the vibrancy of the color, the tone, contrast and the comparison of all colors used together.
If you are interested in learning more, here is a great article that covers this topic in much greater detail: How to Create the Right Emotions with Color in Web Design