The field of prebiotic chemistry has been dedicated over decades to finding abiotic routes towards the molecular components of life. There is nowadays a handful of prebiotically plausible scenarios that enable the laboratory synthesis of most amino acids, fatty acids, simple sugars, nucleotides and core metabolites of extant living organisms. The major bottleneck then seems to be the self-organization of those building blocks into systems that can self-sustain. The purpose of this tutorial review is having a close look, guided by experimental research, into the main synthetic pathways of prebiotic chemistry, suggesting how they could be wired through common intermediates and catalytic cycles, as well as how recursively changing conditions could help them engage in self-organized and dissipative networks/assemblies (i.e., systems that consume chemical or physical energy from their environment to maintain their internal organization in a dynamic steady state out of equilibrium). In the article we also pay attention to the implications of this view for the emergence of homochirality. The revealed connectivity between those prebiotic routes should constitute the basis for a robust research program towards the bottom-up implementation of protometabolic systems, taken as a central part of the origins-of-life problem. In addition, this approach should foster further exploration of control mechanisms to tame the combinatorial explosion that typically occurs in mixtures of various reactive precursors, thus regulating the functional integration of their respective chemistries into self-sustaining protocellular assemblies.