I think it would be impossible to find a group of unbiased individuals. Therefore the only solution is to base district lines on some completely unbiased measure, such as grid or population map. If we take the decision out of the hands of politicians and make it arbitrary, it won't be perfect but at least will not be directly influenced.
I disagree with the previous statement. On a commission like the 9/11 Commission, it does make sense to have people who once held office but no longer do. By contrast, a redistricting commission should not really be a political body so there is no need to have politicians on such a commission. In fact, I believe that having ex-politicians on it will undermine public trust -- the public will not believe the officials have any motives other than helping their own party.
I think that this is why people who have been in office are specifically barred from California's redistricting commission:
However, an applicant is ineligible to serve on the Commission if the applicant has a “conflict of interest” as defined by the Act. An applicant is ineligible if, during the 10 years prior to submitting an application, the applicant, or a member of his or her immediate family has:
Been appointed to, elected to, or a candidate for a California congressional or state office;
Served as an officer, employee, or paid consultant of a California political party or of the campaign committee of a candidate for California congressional or elective state office;
Served as an elected or appointed member of a political party central committee in California;
Been a registered federal lobbyist;
Been a lobbyist registered with the State of California or a California local government;
Served as paid California congressional, legislative, or State Board of Equalization staff; or
Contributed $2,000 or more to any California congressional, state, or local candidate for elective public office in any year.
I would say that what you need is people who are respectable and perhaps educated, but who have no connection to politics. Redistricting should be a technical process, not a political one.
I would say that the people who are best qualified to be as unbiased as possible on panels or commissions would be those who are no longer in the sphere of elected officials. They should be individuals who understand the demands of political office, but would be able to render their opinions without the need to have to acquiesce to public opinion in order to save their jobs. For example, if we look at the individuals that comprised the 9/11 Commission, we see individuals who are no longer in the public sector, but understand the realities of it. Figures like Thomas Kean, former Governor of New Jersey, or Bob Kerrey, former Senator from Nebraska, or James Thompson, the former governor from Illinois. We can see that these individuals will fully understand the need to be accountable to the people, but without the demands of being currently in political office. In my mind, individuals who understand the public demands but do not have to be beholden to them while delivering their opinions on a commission would be the best individuals to serve in an unbiased capacity.