What's the range of your signals?
Arduiono straight up has 10 bit ADC with 1 LSB limit of 5V/1024 or 1.1V/1024 if using the internal reference.
If you'l need better precision, then adding an external ADC will be needed.
A standard Uno type Arduino has 6 channels of analog going into a MUX for reading one at a time.
A 1284 based board has 2 more inputs, into the same mux.
A board like my "Bobuino" is 1284 based, also has and SD card for logging, and a Real Time Clock for recording the time of the samples with 1 second accuracy.
And you can add an ADCshield if you need more precision.
Writing the code to check for a minute passing, taking the 6-8 whatevever samples, and storing to the SD card would not be that difficult.