The classic PIC used in data loggers is the 16F877, which is a 40 pin PIC, this easily gives you up to 8 analogue input channels, connections for I2C EEPROM, a serial port, and an LCD display, plus spare I/O for buttons and switches.
But depending on your exact requirements a smaller PIC may be fine, any with A2D is all you need, and enough pins for what you want - there's no need for a PIC with hardware I2C, it's easily done in software.
My PIC tutorials include almost everything you need!.
I presume the EEPROM you mentioned is a 24LC512 (not a 515), giving 512 kbits of storage. You can use multiples of them to increase capacity.
For the period you simply wait 1 second, do the three samples, then wait again - it's probably best to use a timer interrupt for that!.