Start with a microcontroller AND a FPGA or it's simpler CPLD cousin of some type. Learn how to use both of them and understand what your doing with both of them. Look up the Altair! You know, the world's first PC. Find stuff that was popular in the beginning of the computer age. See how hardware Pong was made. Try and see if you can recreate it on that microcontroller. After that, see if you can recreate it on the CPLD. It will you some idea about what your about to embark on.
From there, try taking on a communication protocol. Ask around for something simple you can learn in a month.
By this time you will hopefully have enough knowledge to give Bluetooth a shot and then see exactly how big a divide there is between the hardware and software world and how much stuff was "hidden" from your view.
Good Luck