Switching gains on a precision operational amplifier using a microcontroller
Low noise is the goal.
Assume a 62 ohm total of all the front end noise sources.
That produces 1.0 nanoVolts per rtHz noise density.
I suggest you have a low_noise first_stage, followed by a switched_gain second_stage.
Most important is what is the BANDWIDTH? If 100Hertz (actually 100 /(pi/2)), then the total input_referred_noise will be 1nanoVolt /rtHz * sqrt(100) = 10 nanoVolts RMS (or about 60 nanoVolts PeakPeak at the 1ppm level).
Thus 10 nanoVolts RMS, in 100Hz bandwidth, is about the lowest you can reasonly do.
Notice the switching_gain burden is NOT in the first stage, but the 2nd stage.
For gain_switching, you have numerous choices, because of the gain of the first stage provides a Gain_1 * Gain_1 advantage. Thus Gain_1 of 10 will reduce the impact of Stage_2 noise by factor of 10 * 10.
But how serious about low_noise must you be?
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If you want DC_stability (low DC drift), then designing the PCB, with thermal_shorts and thermal_opens, becomes a easy learning curve.
At the 10 nanoVolt floor, you need to block or design_out incoming interferers from

electric fields, coupling onto ALL circuit nodes

magnetic fields (60Hz; spikes on 60Hz; switch_reg transients at 100 nanosecond that are minimally attenuated by copper foils)

VDD trash and even VDD as a feedback path for sustaining oscillation

Ground Plane coupling from OUTPUT back to INPUT, this causing echoes and thus settling time degradation; also any 1mA currents thru 2 squares of standard thickness copper foil will produce [1mA * 0.001 ohm == 1 microvolt error]


You can easily have a millivolt or 10 milliVolts of HFI or EFI.