Statistical modeling of rainfall is an important challenge in meteorology, particularly from the perspective of rainfed agriculture where a proper assessment of the future availability of rainwater is necessary. The probability models mostly used for this purpose are exponential, gamma, Weibull and lognormal distributions, where the unknown model parameters are routinely estimated using the maximum likelihood estimator (MLE). However, presence of outliers or extreme observations is quite common in rainfall data and the MLEs being highly sensitive to them often leads to spurious inference. In this paper, we discuss a robust parameter estimation approach based on the minimum density power divergence estimators (MDPDEs) which provides a class of estimates through a tuning parameter including the MLE as a special case. The underlying tuning parameter controls the trade-offs between efficiency and robustness of the resulting inference; we also discuss a procedure for data-driven optimal selection of this tuning parameter as well as robust selection of an appropriate model that provides best fit to some specific rainfall data. We fit the above four parametric models to the areally-weighted monthly rainfall data from the 36 meteorological subdivisions of India for the years 1951-2014 and compare the fits based on the MLE and the proposed optimum MDPDE; the superior performances of the MDPDE based approach are illustrated for several cases. For all month-subdivision combinations, the best-fit models and the estimated median rainfall amounts are provided. Software (written in R) for calculating MDPDEs and their standard errors, optimal tuning parameter selection and model selection are also provided.