When the menorah is on display between lightings, should it be empty or full (of candles)?
Some have the custom of preparing the Chanukiya in the morning for the evening (this goes for every day, except Shabbat, of course). This not only serves the practical purpose of being ready to light on time without delaying to set up later, but it also commemorates the practice in the Beit HaMikdash called Hatavat HaNeirot, whereby the Kohen (Gadol) tended the Menora and prepared it in the morning for kindling in the late, late afternoon. Since our lighting on Chanuka directly commemorates the lighting of the Menora in the Beit HaMikdash, this suggestion provides a nice “added touch” to the mitzva and symbolism of Chanuka lighting.
This Temple practice of "Hatavat HaNeirot," preparing the lights, actually had a holier status than actually lighting them, as only Kohanim were authorized to do the former, whereas any Jew could technically do the latter. R' Michael Rosensweig, in an essay that examines this and many other details of the Temple menora, suggests that the early preparation of its lights contributes to an overall message of constancy of service of God, and that this message is particularly well-suited to Chanukah:
These themes resonate particularly on Chanukah. Jewish spiritual life was endangered precisely by the effort to disrupt the continuity, constancy and comprehensiveness of halachic life. Particular mizvot and halachic institutions were targeted, undoubtedly also with the purpose of eviscerating the unity and integrity of halachic life. A piecemeal and disjointed avodat Hashem constitutes a corruption of the ideal of halachic life and poses a significant spiritual risk, warranting a rebellion. Moreover, Greek ideology itself promotes the idea of compartmentalization and the fragmentation of spiritual forces and authority, a perspective totally incompatible with Torah life.
With this concept in mind, it seems to me that keeping one's menorah in a state of readiness for lighting all day long could serve as a meaningful extension of the menorah's potency as a symbol of Jewish dedication.
Nitei Gavriel Chanuka 23:15 says that there are those that put in the wicks and oil in the evening when the proper time for lighting has arrived. (Rabbi Aaron M'Karlin, Kamarna, Kaliver Rabbi).
This would indicate to me that there is no problem to prepare earlier if one wants, although it is preferable to do it immediately prior to lighting.
As per my answer at "Prepare your Menora before Shabbat!" there are those that actually hold the reverse is true, and that it is better to prepare as soon as possible.