Hi,
I agree: If you have experience with AVR, then use them. There are so called "pico power" AVRs for low power consumption. For sure only during "power down" --> software controlled. Read AVR "low power" application notes.
GPRS: There are cheap SIM800 Modules. They should be supported by Arduino.
The rest:
Without values nobody can tell whether it can work with microcontroller X or not.
ADC: Resolution, sample rate
LOG: Log rate, datasize per item, time
SEND: data rate, protocol ...
Klaus