How to measure electrical noise?
Noise is difficult to measure, and the amplitude you see on your your scope is only a first indication of the level.
Do you want to measure absolute noise levels, or just comparative? In the latter case the scope could be a good instrument, but at the given levels the average $500 scope will have so much noise itself that any measurement becomes in fact meaningless. You need a high quality scope + ditto probes to do this. 

The difficulty with measuring noise is that it has a wide bandwidth continuous energy spectrum (the continuous spectrum makes it hard to separate noise from signal, notch filters may work). Ideally you measure the noise energy through RMS-to-DC conversion. This is not for the faint-of-heart, as your RMS-to-DC converter has to be very sensitive due to the low levels, and wideband. And of course be low-noise itself! Liquid nitrogen helps :-).
In any case, absolute signal-to-noise ratio is not as easy as reading amplitudes.