You shouldn't have any trouble. Make sure the PIC you choose has a UART and use the UART pins for simplicity sake, otherwise you will end up fiddling with an assembly software UART.
what is this? 1994?
Nah, kidding. i have a product that is just an uart "switch" that i wanted to be the cheapest possible so i went on with software uarts all over the place
yeah, no kidding: having to fiddle with i2c, the baseline is out of the question so you have at least one uart and one mssp (spi/i2c)...
Anyway, if the chip has an EEPROM or self programmable flash, so again, everything beyond the baseline, save the data there, and reload!
my usual software has (this is platform independant)
-a table of default settings, written in flash.
-if one cell of the internal/external eeprom doesn't have a specific value (different than 255, the erased state) write the default settings into internal/external eeprom
-load settings from eeprom in ram for use
then the communication protocol in uart has commands to
-read location x of ram (pointing at settings memory)
-writing location x of ram with data y (pointing at settings memory)
-storing ram into eeprom, as eeprom can be written a finite number of times
and you just do this. when you receive a character you put it in a buffer and compose your message. then a routine analize the message and decide if it's valid and then excecute the action
However, this PIC doesn't have built-in multiply and divide hardware. You should not attempt your project with a PIC that doesn't have the math hardware.
that's true only if you want to do floating point.. or you have tight regulation cycles. i have
many products using pic16/pic18 doing a bonanza of 16/32 bit math, including divisions. who cares? the sample rate is in the lowe kHzr range, the signal is in the Hz - tens of Hz range. if it takes 500u/1ms to complete the whole calculation loop nothing happens.