PIC Questions

[Sandy]

I have a  questions on that cabapilites of the PIC line of processors, here
is what I'm looking to do hardware wise, might you think it can be done
with a PIC and some additional hardware.

LCD Display (probabally 4 bit interface)
RS232 Interface
16 Outputs (via 2 74HC595's)
8 Inputs (via 74HC165)
Input for a rotary encoder (2 inputs)
2K of  Data Storage User Programmable
(Maybe 93C86 or 24C16 Serial EEPROM)

What might I be looking at as far as PIC part. Looks like 3 serial devices,
and 2 Input pins, and 2 I/O for RS/232. Is a configuration like this
possible, comments etc.

Thanks, Sandy