I believe that an increase in min. wage to $13/hr would require big businesses to be responsible, and take care of their employees. The increase would allow the government to spend more money on areas like education by decreasing the amount of money needed for welfare. Although I think welfare is a good program, big business should be the ones responsible for providing their employees with a means to survive, AND thrive.
Additionally, it is not reasonable to increase the wages in one fell swoop, as this could damage businesses, so I suggest a steady increase over 3-5 years.
Finally, I suggest a 2nd minimum wage for smaller/newer businesses in order to not deter entrepreneurs from starting their own businesses. However, as revenues increase, their wages would have to increase as well.