No current limiting required; the circuit will draw only the current that it needs.
You will be wasting a lot of power in the 7805. Say your PIC board draws 100mA which means it requires 5*0.1=0.5W. The voltage drop across the 7805 will be 12-5 = 7V. The same 100mA flows through it, so it will be dissipating 7*0.1 = 0.7W, which means it requires heatsinking, making the overall efficiency 0.5/(0.5+0.7), or 41%.
It would be better to start with a 6V battery, and use a low-dropout regulator (not a 7805). Another way to up the efficiency is to use a switching regulator like a 34063, which would up the overall efficiency to ~90%, meaning that you would only be drawing ~46mA from the battery (instead of 100mA).