For ultra-low input voltage it is better to use so-called "Rail-to-Rail in" op-amps. The point is that with very low voltages the noise will be sow huge that the op-amp can't work effectively at all. Rail-to-Rail amplifiers have very good dynamic range that they can amplify signals almost from -V to +V.
For high frequencies the op-amp must have high cutoff frequency because the gain decreases when frequency increases.
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