Being a new electrical engineering student, I don't have any experience with microcontrolers. What would be a decent starter one?
For starting, I would recommend something popular, purely because of the amount of available information and help. PIC, AVR (and to a lesser degree) MSP430 would probably be the obvious choices, and maybe an ARM Cortex. For MSP430, the Launchpad might be a cheap way to start (memory and flash is somewhat limited, however), for ARM Cortex the STM32 Discovery or LPC Xpresso are options (but more expensive). All include a micro, a demoboard, a programmer/debugger (to load your code into the MCU and step through the code) and an IDE/C Compiler. I think Microchip has a bundle of a Pickit and a demoboard. Not sure what the AVR equivalent would be, maybe a Butterfly or MEGA-1284P Xplained? None of them include a debugger, though.
For an EE student, I would probably recommend learning C (if you don't know it already), since you're unlikely to use BASIC or Wiring (Arduino language) for courses or professional work. Since at least one course involving microcontrollers is likely to be part of your curriculum, it might be a good idea to find out which MCU they use.