TI OP solution (G=1000 or high gain)

This needs more information:

1. Measurement bandwidth (upper and lower frequency)
2. Source impedance (resistance and capacitance)
3. How much loading can the source handle?
4. Power available for the amplifier (voltage rails and current consumption)

I have designed amplifiers with gains of 100x or 1000x and input referred noise levels of 3nV/root(Hz) or less for low impedance sources. However, your ability to meet your requirements is going to be very dependent on the measurement bandwidth.

Quick check...you say your source has a noise level of about 10uV (I'm assuming this is RMS). To keep the amplifier from having too large an effect, it would need to have a noise level 3-5 times less (noise adds by the sqrt of the sum of the squares), so about 2-3 uV rms input referred noise. Divide this by the square root of the measurement noise bandwidth (assuming a purely flat response) and if the result is less than about 2nV/root hz you may have an impossible problem. Keep in mind a 50 ohm resistor is ~0.9 nV/root hz and so 2nV/root hz is equivalent to a single 240 ohm resistor so use care in selecting your opamp resistors. I'm also ignoring any current noise contributions at this point as I don't know your source impedance, but current noise could possibly complicate this.

You refer to a "voice line" so I'm thinking your bandwidth is ~10 kHz. 3 uVrms/sqrt(10kHz*1.57) is 24 nV/root hz. If your source impedance is low this should be easy.

Assuming you can get some gain in the first stage without degrading the SNR, you will likely need subsequent gain stages to obtain a gain of 1000 if your bandwidth is higher than the first stage can support (GBW limitation). However the subsequent stages are easier to design because they see a low source impedance and have relaxed noise specs due to the first stage gain.

Good luck!

Tim