You would look for someone with experience in the area you want to operate in, or maybe someone from a complementary sector. The role of the board is to look at the company in the larger context, i.e. within its market at large, and within its general industrial sector. You also want someone who has a good track record hiring executives, so that they can broaden the circle of people the CEO might hire from.
Your investors, by their virtue of having money, don't necessarily have experience in your specific market, so it's good to bring outsiders that are more interested in seeing the company succeed period, rather than maximizing their own investment, as investors are.