How to select gain for an amplifier before ADC?
Your signal is buried in the noise. Assume you band limit your input in a 200Hz bandwidth.

$$
V_{n(rms)}=5 \times 10^{-4}V/\sqrt{Hz} \times \sqrt{200Hz} \approx 7mV
$$

Your input SNR

$$
V_{in} = 8mV\\
SNR = 20log(\frac{V_{in}/\sqrt{2}}{V_{n}}) = -1.9
$$

When you amplify your signal, the noise will be amplified too. You may need a lock-in-amplifier.



Update:

Thanks @Brian Drummond, i think i should complete the math for you :).

Assume the noise are white noise, the amplitude should be Gaussian distribution. It's common practice to take the peak-to-peak value of Gaussian noise to be 6.6 times the rms value, since the instantaneous value is within this range 99.9% of the time.

$$
V_{n(p)} = 3.3 \times V_{n(rms)} \approx 23mV
$$

The gain allowed without make the ADC input saturated:

$$
G_{max} = 1.5V / ( V_{n(p)} + V_{in} ) \approx 48
$$

Because the 3.3 is statistical value, you may choose a gain less than this.