Amplifying a nV signal across a small resistance
The spectrum of interest is important : some otherwise very good amplifying devices have extra high noise at frequencies below 10Hz.

Two options are worth considering : the first is bipolar transistors to provide useful gain before an opamp second stage.

Why not go straight to an opamp? They are pretty noisy, very few have input noise voltage below 1 nV/rtHz, and you want to do better than that.

PNP transistors are preferred, thanks to their lower base spreading resistance. One example with a good reputation some years ago was the 2SC2547, datasheet still available here... 

Looking at the contours of constant noise figure on page 6, which helpfully plot 2dB and 4dB contours, but not the most useful 3dB, so you have to interpolate between them. But the 1 kHz plot shows a minimum in teh noise at Ic=10mA, with 3dB noise figure with a source resistance between 10 and 20 ohms - call it 15 ohms.

That implies that this transistor, at Ic=10mA, can be as noisy as a 15 ohm resistor - at or above 1 kHz. Note curves for 120Hz and 10Hz allow you to choose a different working point if lower frequencies are important.

Johnson noise ( from Wiki) can be calculated as

0.13 * sqrt(R) nV/rtHz.

So, 0.9nV nV/rtHz would be the noise of a 48 ohm resistor, while this transistor (or a 15 ohm resistor) would give 0.5 nV/rtHz.

I have used it in microphone amplifier input stages, in a typical mic amp input configuration (long tailed pair, current source feeding both emitters, 470R or 1K in each collector{ feeding an opamp, and it does what it says on the tin.

Less exotic PNP transistors like the humble BC214 or newer may do reasonably well too.



The second option, if the spectrum of interest doesn't include DC, is a step-up transformer to match your source impedance to the noise impedance of your chosen amplifier.

For example if you choose the NE5534A with 3.5nV/rtHz, or a noise impedance of 700 ohms, and your source impedance is 1 ohm, you need an impedance transformation ratio of 1:700, or a voltage transformation ratio (turns ratio) of 1:26 (sqrt(700).

The transformer's primary resistance is a noise source of course : it should be relatively few turns, and large diameter wire, to keep the resistance (and hence noise) down. The secondary resistance matters too, though its noise is added on top of the stepped up secondary voltage.

Noise impedance matching allows you to get the best performance out of whatever amplifier you choose.