Cytokines and growth factors are critical regulators that connect intracellular and extracellular environments through binding to specific cell-surface receptors. They regulate a wide variety of immunological, growth, and inflammatory response processes. The overall signal initiated by a population of cytokine molecules over long time periods is controlled by the subtle interplay of binding, signaling, and trafficking kinetics. Building on the work of others, we abstract a simple kinetic model that captures relevant features from cytokine systems as well as related growth factor systems. We explore a large range of potential biochemical behaviors, through systematic examination of the model's parameter space. Different rates for the same reaction topology lead to a dramatic range of biochemical network properties and outcomes. Evolution might productively explore varied and different portions of parameter space to create beneficial behaviors, and effective human therapeutic intervention might be achieved through altering network kinetic properties. Quantitative analysis of the results reveals the basis for tensions among a number of different network characteristics. For example, strong binding of cytokine to receptor can increase short-term receptor activation and signal initiation but decrease long-term signaling due to internalization and degradation. Further analysis reveals the role of specific biochemical processes in modulating such tensions. For instance, the kinetics of cytokine binding and receptor activation modulate whether ligand-receptor dissociation can generally occur before signal initiation or receptor internalization. Beyond analysis, the same models and model behaviors provide an important basis for the design of more potent cytokine therapeutics by providing insight into how binding kinetics affect ligand potency.