Question: I see different people lighting their menora at different times. What is the optimum time?
Answer: The Gemara (Shabbos 21b) writes that the proper time for lighting the Chanuka light is at shekia, the setting of the sun. There is a considerable range of opinions regarding exactly what this means.
According to Rambam (Chanuka 4:5) this means the beginning of shekia. Thus, the Vilna Gaon (Biur Hagra OC 672:1) writes that one should light at sunset while the Rema (Darkei Moshe OC 672:4) writes that the Maharil would light just after sunset.
Other poskim however, write that the Gemara refers to the end of the process of the sun setting, tzeis hakochavim. The Mordechai (Shabbos 455) writes that one should wait until tzeis to light as candles are more noticeable during the night. The Tur and Shulchan Aruch (OC 672:1) rule like the Mordechai (See Rosh, Shabbos 2:3; Tosafos, Menachos 20b; Bach OC 672:1; Magen Avraham OC 672:1).
The Mishna Berura (672:1; Biur Halacha 672:2) quotes both opinions and writes that those who daven maariv at tzeis should ideally light first, though should ensure that there is enough oil to last until a half hour after tzeis.
Similarly, R’ Moshe Feinstein (Igros Moshe OC 4:101:6) writes that the ideal time to light is about ten minutes after shekia though one should ensure that there is an hour’s worth of oil.
In conclusion, there are different minhagim as to when to light with some lighting at shekia and some waiting until tzeis hakochavim. Those lighting earlier should ensure that there is enough oil to last for half an hour after tzeis hakochavim.