We use angle-resolved photoemission spectroscopy to study the doping evolution of infinite-layer Sr$_{1-x}$La$_{x}$CuO$_{2}$ thin films grown by molecular-beam epitaxy. At low doping, the material exhibits a dispersive lower Hubbard band typical of the superconducting cuprate parent compounds. As carriers are added to the system, a continuous evolution from charge-transfer insulator to superconductor is observed, with the initial lower Hubbard band pinned well below the Fermi level and the development of a coherent low-energy band with electron doping. This two-component spectral function emphasizes the important role that strong local correlations play even at relatively high doping levels. Electron diffraction probes reveal a ${p(2\times2)}$ surface reconstruction of the material at low doping levels. Using a number of simple assumptions, we develop a model of this reconstruction based on the polar nature of the infinite-layer structure. Finally, we provide evidence for a thickness-controlled transition in ultrathin films of SrCuO$_2$ grown on nonpolar SrTiO$_3$, highlighting the diverse structural changes that can occur in polar complex oxide thin films.