You must chose a PIC with enough pins for your F2F devices, two pins for the EEPROM (C or LC still require two lines regardless which one you chose), and however many additional pins for external communications or other connections. Remember one of the pins on the 12F675/683 is INPUT ONLY that leaves five I/O's. If you are going to use Serial Communications (like RS232) then you WILL need a Crystal or Resonator, that will use up two pins, and three I/O's may then be insufficient for your needs.

As regarding EEPROMS... the 'C' device is a plain SERIAL device requiring something like SHIFTIN/SHIFTOUT usage, whereas the 'LC' is an I2C BUS device requiring I2CWRITE/I2CREAD usage.