You program the chip for power consumption by lowering the voltage and speed and/or using sleep mode and/or turning off parts you don't use. AVR chips with P at the end of the name are branded "pico-power" because of power saving options.
GSM and other addons usually require libraries and some RAM. Stack enough up and you will not be looking at the cheapest chips regardless of the board. Chip size is not directly how much power uses either, they sleep about the same and the running power isn't greatly different at the same clock speed.
But since you are looking for ready made software it would be best to get that and the hardware to match.
Other questions, save for if you will have to choose your own and start a development project that can take months.