What about Arduinos makes 10mV/div insufficient? Logic level is 500 divs. If you're doing sensitive DAQ, you're probably better off testing it at larger signals (where distortion will be more exaggerated) and assuming it's fine at lower levels, using the DAQ itself to provide the data for analysis to confirm this (which will probably be easier than measuring it on the scope -- you can do the analysis on the MCU directly, or prepare and copy an array via serial and process a .CSV or what have you).
Residual noise (noisy signal chain, switching supplies..?) might still be of interest, but this can at least be measured by the same methods, if not so easily tracked and troubleshooted.
To get practical 1mV/div use, you can get a 1x or switchable probe (however: mind the limited bandwidth -- read the spec sheet for that gotcha!), a preamp or probe extender, or connect coax directly to the circuit (assuming it doesn't mind the capacitive load and reflection, or the extra loading if 50 ohm terminated), or using a buffer (to keep the gain but eliminate the loading). Speaking of noise, be mindful that such levels are very sensitive to ambient and conducted radiation (nearby radio stations can peak over 1mV in unlucky situations), so pay very close attention to grounding, shielding and lead dress.
Also mind the limitations of bandwidth: typically a scope of that bandwidth will have maybe 0.2mV RMS baseline, mostly from the noise of a 50 ohm source. I believe Rigols aren't usually that good, and have some excess noise beyond that. A preamp in front (even with a low noise factor) will magnify the source noise, only making it worse (though not necessarily worse than the excess noise of the scope already).
You can discard a lot of noise by narrowing the bandwidth (lower bandwidth setting, or "hi res" or averaging modes, or analog filtering the signal before the scope), but this may discard useful signal information as well. If your signal is periodic, you should trigger or sync from a much stronger related signal, then use averaging to remove noise unrelated to the signal (this correlates the signal, "pulling it out of" the noise).
This is also helpful on older scopes that used software magnification for the lowest ranges (HP 54600B comes to mind). Quantization noise remains, but averaging can remove that noise (just as it works with any other noise source), getting a smooth signal back out. If you were hard pressed for resolution, you probably can't do this on the Rigol itself, but could save a CSV and do the math in a spreadsheet or MATLAB/Octave for the absolute finest resolution. (The latter also has the benefit of quickly and easily doing spectral and statistical studies, like autocorrelation.)
Tim