Edited on 15th,Aug
Tradoffs between ADC range and amplifier gain
If I want to measure a very small signal with 16 bit ADCs，say 10kHz sine waves with amplitude ranging from 0 to 1uV, I have to amplify the small signal first. The signal should be amplified with peak-to-peak value equal to the range of ADC. Then the signal will be shifted up by half of the ADC range by an ADC driver(with level shifter).
My questions is: What are the trade offs between amplifier gain selection and adc range?
Should I use a 2.5V range ADC(16 bit) with 1,250,000 gain amplifier, so the peak-to-peak value of the largest sine wave(1uV) will be amplified to 2.5V?
Or should I use a 5V range ADC(16 bit) with 2,500,000 gain amplifier, so the peak-to-peak value of the largest sine wave(1uV) will be amplified to 5V?
What aspects should be concerned in the decision?
How to choose ADC number of bits?
Also a question, how should I decide the number of bits to use? The noises are fairly large, but I am going to use signal processing techniques, which can reduce noises greatly. It means that more bits should still be useful. (Thanks to gbulmer, you made me realize that I did not really think about this question..)