This is a great question for good corporate governance. An independent board member (or "outside director") is like all other members of the board, making decisions to serve the best interest of the shareholders as a whole -- except that outside directors are intentionally free of all affiliations, financial interests, and other ties which might bias the director and prevent him or her from exercising completely impartial judgment with regard to any matter before the company.
For this reason, outside directors do not hold operating roles with the company. Ideally they will not have strong ties (and certainly no fiduciary duty to) any one group of investors or other shareholders in the company (including founders). Outside directors often own minimal stock or equity in your company, sometimes taking sitting fees as their only compensation. They should have few financial or operating relationships with your company’s immediate trading partners. They may even be drawn from completely different industries, freeing them to render perspectives and exercise discretion that other members of the board may not be capable of delivering.
The "best" candidate for an outside director position will be highly specific to your firm - taking into account its industry, its stage of maturity, its exposure to risks and opportunities, and its ability to attract prospective board members.
Corporate governance is an interdisciplinary endeavor. In addition to any business requirements that you might apply to your organizational strategy and to the election of an outside director, you will also want your corporate counsel's advice when defining the ideal profile of an independent board member for your company.
I hope that helps!