Microbial cells are able to reach balanced exponential growth in a variety of environmental conditions. At the single-cell level, this implies coordination between the processes governing cellular growth, cell division and gene expression. A fundamental goal of microbiology is to build a quantitative and predictive understanding of how such coordination is achieved. It is known since long that the size of E. coli cells grown in media of different nutrient quality increases with growth rate. Recent data, however, shows that this relationship is of another nature when growth is modulated by other types of limitations, such as translation inhibition or forced expression of useless proteins. Here, we present a single-cell coarse-grained model of bacterial physiology that unifies previous efforts (i.e. the proteome allocation theory and the structural model of division control) into a simple and low-parametric model. We show that this model quantitatively explains the observed relationship between cell size and growth rate for various types of growth limitations with a single free parameter. In addition, predicted proteome fractions agree with observations, and when noise is included in the model, the recently discovered adder principle of cell size homeostasis is correctly predicted. Thus, our minimalistic coarse-grained model successfully recapitulates the most fundamental aspects of bacterial physiology, and could serve as a guide for the development of more detailed and mechanistic whole-cell models.