Should you have a board of directors? What kind of people should you ask to join a board of directors?
It depends on how you structure your business and constitution, whether you have non-exec and exec board directors who carry liability vs a less formal advisory group. In either case you want diversity of experience and gender. Ideally they will have completed the company directors course, know the rule of nose in fingers out, be able to read your financial reports, govern appropriately and help set your strategic direction. Think about your business goals, your gaps in experience and knowledge, who you buyers are and also your culture and leadership style. A CEO and Chairman need to work well together and your board needs to understand your market, buyers and product fit. Maybe you need an impressive name to help raise capital or someone with international experience to guide your global expansion. Don't rush into this, think carefully about terms, get advice and if you do establish a board be professional with their need for due diligence, letters of appointment, setting expectations and board reports.
It all depends on the size of the company, but as a starting point I would be looking for members that had proven business experience and were experts in their field of management. You might also invite investors onto the board due to the contribution.
I would add that at the very least to have some mentors to keep you going in the correct direction. Again as Annette said, look for a diverse group to guide you. Whether or not you decide to have a formal board of directors will depend on your business, but you should always have a mentor or two in your back pocket.