How much bandwidth do you need?
I'm only measuring voltage rails on a device-under-test to determine whether their levels are in-spec, not any kind of varying signal, so hardly any bandwidth at all.
If not much, you might average it all out on the digital side and kinda not care. It's not a great solution, as the noise will alias and there is an asymmetry to it (it's ratiometric, in particular in the denominator, not additive), which will cause some wandering baseline that doesn't average out, but it might be small enough not to mind (i.e. consider the effect of 3.35 vs. 3.25V ref).
I might do some averaging on the digital side, not sure yet. Although, I want to ensure the voltage rails under test aren't fluctuating so averaging over too much of a period will probably mask what I'm trying to measure. What I'm probably going to be looking at is not only the mean value of samples but also their std. deviation too.
What spectrum is the noise? If it's switching noise, an LC filter is fine. If it's all kinds of crunchy, from various causes, erratic time constants, likely you need an LDO.
I think it's switching noise from a DC-DC converter mainly. No idea what frequency the switcher is running at. I should probably try and analyse it in more detail than I've done so far: that is, poke it briefly with the 'scope and go "ew, that's dirtier than I was expecting".
Note the LDO can be very thin: say 3.0V, so logic levels aren't violated. You don't want e.g. 3.6V+ beginning to forward-bias the ESD clamp diodes into a device at 3.0V supply, or 3.3 into 2.7, but 3.3 into 3.0-3.1 would be perfectly fine. Downside: LDO PSRR is typically trash to begin with, and it's even worse operating so close to dropout. Again, it's only a thing if you need low frequency filtering.
Bonus: LDO at least gives [the chance for a] more accurate supply/ref, potentially reducing calibration error.
I suppose an additional benefit of running the ADC and op-amps from a 3V supply is that I'll also get slightly higher resolution, as the input will be larger relative to the reference. But that's minor, and I don't particularly need super accuracy - even this 12-bit ADC is a bit overkill for my application.
I wouldn't know how to pick an LDO regulator with good PSRR, though. It seems difficult to make comparisons because the manufacturers all give specs according to different conditions. Some give it at 1kHz, some at 100kHz, etc. I'm not even sure what magnitude of PSRR is good. Is 50 dB good or poor? 70 dB? 90 dB?