Maximising sensitivity of AC voltage measurement on top of DC voltage with Arduino ADC
You can make an analog precision rectifier and read the resulting filtered DC voltage if you are not interested in the waveform. Average voltage of a 1V peak sine wave after full-wave rectification is (2/\$\pi\$)V ~= 0.637V. Add some gain and/or decrease the ADC reference voltage to optimize the range for maximum resolution.
The LM358 is suitable for mains frequency, however it cannot output 5V so you would be better to reduce the reference voltage to 2.56V or 1.1V rather than the default 5V.