medium power BJT being used as a "low noise" device is rather conditional. It appears "low noise" due to sheer die size which lowers it's bulk resistance resulting in what appears to be low noise. Being a Bipolar, it will have current noise dependent on collector current (beta related) adding to this leakage currents can add to this effect making this a very source impedance dependent "low noise" device. Other problems are die size which has an effect on it's BW, collector base capacitance will be high and if used as a common emitter amplifier miller effect will stunt's if frequency response. Both collector-base capacitance and beta modulates with current and temperature changes. All these reasons an more are why medium sized bipolar transistors are not often used if at all for low noise input stages.
Devices like the LM394 would have been use if a circuit needed a device like this. Alternatively, super beta match diff pairs are also use as low noise input devices. Super beta bipolars goes a ways to reducing noise current, but does not eliminate it.
Want to use individual matched FETS or bipolars as a diff pair/ They will need to be thermally coupled to foster tracking. In the case of FETS, their IDSS or VGS will need to be matched over a range of temperature or there can be serious temperature drift problems. This problem is less with bipolars, but not to be ignored. Oh, any thermal gradient between the two diff pair devices aggravated this problem.
As for power supplies, if the circuit cannot achieve low noise (less than 1nV/root-Hz @ less than 100Hz) the circuit design will be difficult to implement into many systems. Designed properly low noise input sections have good power supply noise rejection. Batteries powered low noise input sections regardless of they batteries internal impedance and possible low noise is simply not the way to get there.
Using a coupling capacitor, specially a electrolytic or similar will cause a host of distortion and signal errors at the signal levels being discussed. EE caps have extremely high dielectric absorption (put a volt meter on a few hundred uF EE cap and measure it's voltage. Charge and discharge it and measure it again) and do not behave any where near like a ideal capacitor. If forced to use a coupling capacitor, it must be polystyrene or teflon film with few exceptions.
Noise from grounding is a serious problem that cannot be ignored. The problem is more difficult and more serious for input sections with a chassis grounded-single ended input. If a differential input section is needed, the impedance for both + and - inputs must have the same impedance, frequency/phase response and gain to idealize common mode rejection.
Knowing what the source impedance is makes all the difference to achieving low noise. Designing an input section for a low ohmic value thermocouple is very different than designing a low noise input section for a electrometer, charge amplifier or similar very high impedance device.
Any digital device like a DAC (i.e., DAC in the FB loop) will produce glitches as they make their switching transitions. These glitch transients will find their way back into the input section where they will be integrated by the devices involved resulting in more noise and distortion. This is one of the many reasons why mixing digits with low noise high fidelity analog can be so extremely difficult to do properly.
A "low noise" device is only the beginning to making a good, low distortion, signal accurate low noise input section. More often than not, really good low noise, low distortion, high performance input sections do not come from an IC, these are done the old fashion way using individual devices.
Bernice
The Art of Electronics, third edition, has a very long chapter on low noise techniques. It contains many practical and theoretical results, some of which are well-known, some of which came as a surprise to me.
For example, I would never have guessed that (for some applications) the lowest noise transistor would be a medium power BJT!