Shanghai or Beijing... where to go?

Hi, I'm planning a 3 month trip to china. It will be for the first time. The idea behind this trip is to "test the waters" in order to move there for once afterwards. I'm thinking about Beijing or Shanghai for this attempt...

Do you have any information that could make my trip fruitful?

By the end of the journey I should be well informed about job opportunities - French or English teacher for example, webmarketing, or even music teacher/performer (guitar). I will definitely need to learn Mandarin, so information about language programs in universities would be very welcome as well.

Which city do you think would most fit my plan and why?

Thanks for your help.