Using Arduino for datalogging remote area power supply

No personnel experience with logging.
Suggest a serial EEPROM or FRAM to log the data into.
Or do some math, # of bytes each message type, any protocol/seperators/alignment bytes, how many total samples between uploads, maybe SDcard might be better.
Powered from AC source, yes? Not battery? Maybe just battery as temporary backup?

How will you tell when there is a connection? There will be a message sent over the USB/Serial port saying "Send your data now"?
Or you will have an ethernet, wifi, bluetooth, etc. shield?