Symbiotic stars are long-orbital-period interacting binaries characterized by extended emission over the whole electromagnetic range and by complex photometric and spectroscopic variability. In this paper, the first of a series, we present Optical Gravitational Lensing Experiment (OGLE) light curves of all the confirmed symbiotic stars in the Large Magellanic Cloud, with one exception. By careful visual inspection and combined time series analysis techniques, we investigate for the first time in a systematic way the photometric properties of these astrophysical objects, trying in particular to distinguish the nature of the cool component (e.g. semiregular Variable versus OGLE small-amplitude red giant), to provide its first-order pulsational ephemerides and to link all this information with the physical parameters of the binary system as a whole. Among the most interesting results, there is the discovery of a 20 yr-long steady fading of Sanduleak's star, a peculiar symbiotic star known to produce the largest stellar jet ever discovered. We discuss by means of direct examples the crucial need for long-term multi-band observations to get a real understanding of symbiotic and other interacting binary stars. We eventually introduce BOMBOLO, a multi-band simultaneous imager for the Southern Astrophysical Research 4 m Telescope, whose design and construction we are currently leading.