Protecting an ADC from negative voltage: Is it better use diodes OR to offset voltage?
1) In that circuit, set the collector resistor == Rbase / beta.

This set the DC Vout  to VDD/2.

That suggests 1,000 Ohm in the collector.

2) your circuit will have a gain of 0.5 * ( 5v / 0.026 ) = 0.5 * 5 * 39 = 100x

Thus more than 0.05v input will be clipping (in the rails);

3) for moderate (10%) distortion, keep the input voltage at 4 milliVolts or less

4) the ADC needs to grab a bunch of charge during each sample; you can evaluate the impact of these impulse_functions, by adding 10nF from collector to Ground.