You can easily find opamps with internal Rnoise of 1,000 ohm; such a relatively low noise would show up in the opamp datasheet as "noise density" of 4 nanoVolts / rtHz.
In 100 Hz bandwidth, this would produce 4nV * sqrt(100) = 4nV * 10 = 40 nanoVolts RMS noise.
if your signal is 60dB (1,000X higher in voltage) bigger at input to the opamp, you have
40nV * 1,000 = 40 microVolts input from the sensor. We'll assume the peak-peak is double that or 80 microVolts. For easy math, round up to 100 microVolts PeakPeak.
Your output is to be 10 volts PeakPeak, thus you need gain of 10v/100uV or 100,000X or 100dB.
I'd plan to do this in two stages: 100X and 1,000X.
Opamps are not perfect. They have some input offset voltage. You can easily get 0.1 millivolt worst_case for the 2nd opamp; that opamp gain stage is to have 1,000X gain, thus the output DC will be (worst case) 0.1mV * 1,000X = 0.1 volt.
You MUST insert a DC_block (high pass filter: series cap and shunting resistor) between the two gain stages. A 1 second tau (0.16 Hz F3dB asymptotic corner) can be 1uF and 1MegOhm, or 22uF and 50Kohm. The cap must not be polarized.
S I suggest this:
A) stage#1 has opamp with Rnoise of 1,000 ohms internally (4 nanoVolt/rtHz noise density), and uses a non-inverting gain configuration with 100 ohms and 9,900 ohm. The 100 ohms is from Vin- to GND, the 9,900 ohm is from opamp output pin to Vin-. Your sensor connects to Vin+ of that opamp. You may need RFI/EMI filtering between sensor and opamp.
B) have 1uF between opamp#1 output pin and the opamp#2 Vin+; have 100,000 ohms from opamp#2 Vin+ to ground; this is 0.1 second time constant, or 1.6 Hertz F3dB on the high-pass-filter asymptotic curve (Bode).
C) stage#2 has opamp with Rnoise of 10,000 ohms internally (12 nanoVoltsrtHz noise density); this is not crucial spec. What is crucial is the DC_offset worse_case: find an opamp with 0.1 millivolt (100 microVolts) worse_case input DC_offset. The system design has this stage providing 1,00X gain; use 100 ohms from Vin- to GND; use 99,900 ohm from opamp#2 output pin to its Vin-.
If you truly want this relatively low noise performance, you need clean power supplies. That is another system design issue. What is the PSRR curve, versus frequency, of your opamp#1? of opamp#2? Do not try to use a Switching Regulator to provide these voltages.
Additionally you must design the GROUND PLANE, which connects to the Sensor, the 100 ohms of stage#1, the 100,000 ohms of the DC_block, the 100 ohms of stage#2, the capacitor of the output Low Pass (200 Hz) filter, AND the various power supply capacitors. You may also need a shielded cable to the sensor. You need some output cable or wiring to the ADC (digitizer, or data acquisition system) which needs a Return Wire.
If the output Return Wire is too close to the Sensor Ground, you may get oscillation.
You must design all of these GROUND points.
D) add a final stage: 200 Hertz 1-pole RC lowpass filter, using an R in series into a shunting cap to ground.
E) design the VDD filtering TREE, so the feedback from output to input is adequately attenuated.
AND with all this gain, broadband, the final opamp likely will be overloaded with random noise. Thus you must reduce the bandwidth of each opamp to about 1,000Hz using small capacitors across the Rfeedback resistors. Then use the final 200Hz low pass filter to set the bandwidth.
Can you do this desig without opamps? Sure. A chopper-stabilized amplifier would be fine. Bob Pease wrote of the varactor-bridge input-sampling profit center for Philbrick Nexus, where a 5MHz bridge drive/demodulate oscillator was the key. Then 3 transistors provided AC gain, and some crucial PCB--PCB feedback of the positive nature converted the circuit into a "reflex" amplifier using feedback to boost the open-loop feedback enormously. After demodulation, a single PNP with resistive pulldown to -15 volts was the output.