We present the results of a year-long photometric monitoring campaign of a sample of 23 nearby (d < 60 pc), bright (J < 12) dM stars carried out at the Astronomical Observatory of the Autonomous Region of the Aosta Valley, in the western Italian Alps. This programme represents a ‘pilot study’ for a long-term photometric transit search for planets around a large sample of nearby M dwarfs, due to start with an array of identical 40-cm class telescopes by the Spring of 2012. In this study, we set out to (i) demonstrate the sensitivity to <4 R⊕ transiting planets with periods of a few days around our programme stars, through a two-fold approach that combines a characterization of the statistical noise properties of our photometry with the determination of transit detection probabilities via simulations; and (ii) where possible, improve our knowledge of some astrophysical properties (e.g. activity, rotation) of our targets by combining spectroscopic information and our differential photometric measurements. We achieve a typical nightly root mean square (RMS) photometric precision of ∼5 mmag, with little or no dependence on the instrumentation used or on the details of the adopted methods for differential photometry. The presence of correlated (red) noise in our data degrades the precision by a factor of ∼1.3 with respect to a pure white noise regime. Based on a detailed stellar variability analysis (i) we detected no transit-like events (an expected result, given the sample size); (ii) we determined photometric rotation periods of ∼0.47 and ∼0.22 d for LHS 3445 and GJ 1167A, respectively; (iii) these values agree with the large projected rotational velocities (∼25 and ∼33 km s−1, respectively) inferred for both stars based on the analysis of archival spectra; (iv) the estimated inclinations of the stellar rotation axes for LHS 3445 and GJ 1167A are consistent with those derived using a simple spot model; and (v) short-term, low-amplitude flaring events were recorded for LHS 3445 and LHS 2686. Finally, based on simulations of transit signals of given period and amplitude injected in the actual (nightly reduced) photometric data for our sample, we derive a relationship between transit detection probability and phase coverage. We find that, using the Box-fitting Least Squares search algorithm, even when the phase coverage approaches 100 per cent, there is a limit to the detection probability of ≈90 per cent. Around programme stars with phase coverage > 50 per cent, we would have had >80 per cent chances of detecting planets with P < 1 d inducing fractional transit depths > 0.5 per cent, corresponding to minimum detectable radii in the range ∼1.0–2.2 R⊕. These findings are illustrative of our high readiness level ahead of the main survey start.