Hi,
You have many options to choose from - first the chip, the 18F4550 is a common choice for usb connectivity, if that is a requirement, but also look at other chips like the 3.3v pic24 usb versions.
You really need to have some idea of how many bytes of info you need to store each time so you can actually work out the total space needed for your time period and also into methods of condensing your info the minimise the space needed
EEprom , either onboard the pic chip or external chips may handle the volume and is quite easy to program up.
For larger volumes then an SD card would be the answer, this would have the advantage of being removable as well as being able to usb transmit the data to a laptop.
The downside its the programming is a lot more complex.
See Microchips site for the many pages of free info and code for both the USB and SD card.
A led is a good status indicator, but consder a lcd display, this will give you much better visual control of the comms and also allow you to interrogate the current and stored readings in situ.
As for your ' only need to program the pic once' - don't believe yourself !
You will always find ways to improve your program, so when you design your ciruit make sure you include ICSP - its only a small connector and a cople of cheap components - well worthwhile.