First and very simply, you can check it´s own noise with and without hi-res mode, visually.
Self-noise w/o any input signal is basically THE important thing to check.
It should be checked at different V/div settigs, comparing normal and hires mode at each V/div.
The quantities of interest which should be measured are
- Standard deviation (gives the RMS voltage of the noise as a single number, with DC excluded)
- FFT spectrum of the self noise over the full 0...fs/2 frequency span, on a vertical dBV scale, where fs is the sample rate
Ensure that the FFT sample rate is the same as the capture sample rate (i.e. that neither up- nor down-sampling is involved)
The resolution does not need to be very high, 16k points (for instance) are certainly sufficient.
[ If enabling hires does not lead to the expected amount of noise reduction (and there is a suspicion that it does not), then the key may be spectral power distribution of the noise, so it is advisable to check it. ]
Initially I'd only consider a timebase with the maximum sample rate.
In subsequent steps, slower timebases can be checked too.