I fully second Sam's recommendation. In fact, I was just about to recommend Adobe's color harmonization app myself, when I saw Sam's post.
One very important point: Because of (as Sam mentioned) the subjectivity of color schemes and trends in popular culture, even world-class experts in color harmonization always seek the opinions of people similar to the intended audience for the website. Large design firms will often convene
focus groups to evaluate color combinations (assuming the campaign / contract is big enough). There are just too many ways to "go really wrong" in this area if you are relying only on your own opinions. For example, young users may feel your scheme is "so yesterday", while older users may think your scheme is obnoxious and looks like the colors of a cheap ransom note (see
Wikipedia article on the ransom note effect), and pro web designers will criticize it because it doesn't work with the current trend in
flat user interface design or Google's push for
material design, etc. etc..
Even if you only informally poll your colleagues, wife/GF, and friends, DO NOT risk making a fool of yourself by putting out the first scheme that you happen to like.
That being said, I would strongly suggest that before you jump right into this project, you get a wider perspective on color harmonization. You need to do this to develop your artistic sensibilities w.r.t. color before making any suggestions to anyone about color schemes. For example, at the simplest level, you don't want people suffering from headaches and eyestrain because you put a bright saturated blue right next to a bright saturated red. My suggestion would be that before you do any work on the subject, Google {harmonizing colors} and you will find a huge number of very good articles written on this subject. Carefully read and understand several of them.
Now, back to your particular question ...
Hopefully, you have thoroughly read several articles on color harmonization. Open color.adobe.com in your browser or with an iOS app, and learn how to use it by following along one of the many tutorials on its use, e.g.,
this one.
Immediately, you will see that the major color schemes are all represented:
Analogous
Monochromatic
Triad
Complementary
Compound, and,
Shades
How do you decide between them? You do this by first setting general goals for your color scheme and writing down some adjectives that should describe it, e.g., peaceful, active, nostalgic, avant-garde, looks like the scheme on XXX, etc. etc.
You can then try some of the schemes and see which ones you think will meet your overall design goals and are consistent with the adjectives you came up with.
In addition, so you don't have to start from scratch, if you get yourself an Adobe login, you will be able to scroll through thousands of color schemes that have been developed by other designers, and see if any catch your eye. You can then download it into Kuler, and tweak it to your heart's content.
Finally, I would make a mock-up web page using that color scheme and run it by other folks. For me at least, viewing colors in abstract patches doesn't give me good insights into how these colors will look on a web page. A lot depends on if you will be using a particular color as text, as a complicated graphic element, as a background, the fraction of the page that color takes up, etc. etc.
The best of luck with your project.
Tom M