I was recently looking into the programming kits available for vex, but I found that the prices were somewhat ridiculous (since I am a student, of course). I am wondering if there is any sort of free programming API that could be used instead of the ones sold through vex?
Yes the Vex header files and libraries are available as a download from the Vex site. They are located here You need to download the Vex Starter Code folder which contains all the files you need to get started with MPLAB.
I’d like to recommend the WPILibrary http://users.wpi.edu/~bamiller/WPILib/ as a great place to start. They are a little easier to use than the basic Vex libs. A simple drive the 'bot program is about 10 lines of code.