You gotta base your designs on their brand identity manual. If you are also doing the logo design and branding, then you decide based on the client's input. As soon as you have the main colors set up, you will use them on the website for a consistent branding.
Usually medical websites are on a clean / spacious design, modern style as much as possible. As colors are concerned, blues and greens, although I have seen spectacular designs in teal, purple or even pink. Again, it depends on the brand identity.