It is important when choosing colours for a website to include UX Designers in the process. We are currently working with a client who recognised the need for our early input, including branding and visual style guides.
Part of our initial steps when choosing a colour scheme is that colour combinations are accessible to as many people as possible. We recommend that you think about the colour contrast of text to its background and the colour of links to the surrounding text. There is no substitute for testing with real people, including people with diverse needs (for example, people with colour blindness, which is 1 in 10 men).
Luckily you can use great tools including Adobe Color Wheel and the Accessible Colour Combination threshold feature to demonstrate which colour areas can be seen by those with different levels of vision. It is best to ensure that your text is as accessible as possible before putting it in front of people (be it internal stakeholders or customers).
Of course contrast is not the only consideration, the colours should produce the right physiological and psychological response in your audience too. See our training course Designing for the Human Mind/Brain for more on this.