Within ten days after its election the charter commission shall hold its first meeting, elect one of the members as chair, and adopt such rules for the conduct of its business as it may deem advisable. In the event of a vacancy in the charter commission, the remaining members shall fill it by appointment thereto of some properly qualified person. A majority shall constitute a quorum for transaction of business but final charter recommendations shall require a majority vote of the whole membership of the commission. The commission shall study the plan of government of the city, compare it with other available plans of government, and determine whether, in its judgment, the government of the city could be strengthened, made more responsive or accountable to the people, or whether its operation could be made more economical or more efficient by amendment of the existing plan or adoption of another plan of government. The commission shall consider the plans of government described in this title but shall not be limited to such plans in its recommendations for the government of the city and may frame a charter for any plan it deems suitable for the good government of the city; except that the provisions of such charter shall not be valid if inconsistent with the Constitution of this state, the provisions of this title, or the general laws of the state, insofar as they are applicable to cities governed under this title.