How do we find the right person to manage the content, design and feel of our startup website?
Congrats on thinking through the entire aspect of being a successful website owner.
Your first step is to find a website that you really like--ideally for a company that operates in your industry, but this is not mandatory--then contact the website owner and ask for a referral.
Many happy website owners have been through the mill and have had their fair share of challenges with designers, so they're more than happy to refer you to their designer.
Also, ask your business friends and colleagues if they have any recommendations. As the saying goes, it's not what you know, but whom you know!