GaAs-InGaAs-GaAs core-shell-shell nanowire (NW) structures were grown by gas source molecular beam epitaxy using the selective-area, self-assisted, vapor-liquid-solid method. The structural, morphological, and optical properties of the NWs were examined for different growth conditions of the InGaAs shell. With increasing In concentration of the InGaAs shell, the growth transitioned from preferential deposition at the NW base to the Stranski-Krastanov growth mode where InGaAs islands formed along the NW length. This trend is explained within a nucleation model where there is a critical In flux below which the conformal growth is suppressed and the shell forms only at the NW base. Low growth temperature produced a more uniform In distribution along the NW length but resulted in quenching of the photoluminescence (PL) emission. Alternatively, reducing the shell thickness and increasing the V/III flux ratio resulted in conformal InGaAs shell growth and quantum dot-like PL emission. Our results indicate a pathway toward the conditions for conformal InGaAs shell growth required for satisfactory optoelectronic performance.