Visible light communication (VLC) technology has traditionally emerged as a complementary solution to radio frequency, due to its huge available bandwidth and high data rates. Relying on visible spectrum, VLC allows both illumination and communication, thus representing a green technology with reduced energy impact. However, VLC can also be exploited for localization, and thanks to its huge bandwidth it can reach very high accuracy (i.e., <0.1 m). In this paper, we deal with a VLC network intended as a fully integrated indoor system providing at the same time both illumination, communication, and positioning tasks. Three different optimization problems are presented, aiming to seek for the minimum number of white LEDs that can achieve different constraints of illumination, data rate, and localization accuracy. Different types of LEDs are considered, according to which tasks they are intended to pursue. We consider traditional white LEDs aiming to provide illumination, communication, and positioning; otherwise, we distinguish between devices designed for localization-only and communication-only. Such distinction results in different optimization problems, and related solutions, as confirmed through extensive simulation results.