The actin cytoskeleton is a network of proteins that provides infrastructure for a cell to maintain its shape, divide, transmit forces and enable intracellular transport. We developed and benchmarked a computer program, AFINES, that can accurately simulate the mechanical and kinetic components of this network, including semi-flexible filaments, crosslinkers that bind filaments into force propagating networks, and motors that enable filament sliding and network contraction. Motivated by recent in vitro experiments that controllably combine actin filaments, myosin motors, and crosslinkers, and generate broad structural diversity, we use our simulation to systematically vary molecular properties and densities and outline new structural phase spaces accessible to these assemblies. We test the possible biophysical function of different structures and show tunability of network viscoelasticity and motor transport dynamics. We also elucidate the microscopic processes that produce global contractility in actomyosin assemblies with varying stiffnesses and determine how the mechanical and kinetic properties of filaments and crosslinkers contribute to crosslinker sorting. Together, these results demonstrate how a parameterized computational model can efficiently motivate future experiments and determine the underlying physics of a complex biophysical system.