The best time of day-Zerizin Makdimim Lemitzvos:[1] Although the circumcision may be performed throughout any of the daytime hours of the day[2], nonetheless, Zerizin Makdimin Lemitzvos [those with alacrity precede the performance of a mitzvah to the earliest time possible], and do so at the earliest opportunity of the day, which is in the early morning, [immediately after Shacharis, although not beforehand[3]]. [At the very least, it should take place prior to midday.[4] This applies even by a Mila Shelo Bezmanah i.e. a delayed Bris, that it should nevertheless take place as early as possible in the day.[5] Nonetheless, if delaying the circumcision until later, such as the afternoon, will allow more people to attend, then it is permitted for one to choose to delay the circumcision for this purpose in light of the phrase “Berov Am Hadras Melech.”[6] However, even in such a case, he may choose to do it in the morning in order to oblige by the dictum of Zerizin Makdimin Lemitzvos, and it is not clear that it is better for him to delay it until the afternoon in order to have more people attend.[7]]

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[1] Michaber Y.D. 262:1; Aruch Hashulchan 260:9; Shevach Habris 7:6; See Igros Kodesh 4:154, brought in Shulchan Menachem 5:112; Pesakim Uteshuvos 262:3-4

[2] Admur 444:6

[3] See Aruch Hashulchan 260:9; Pesakim Uteshuvos 262:5 footnotes 27-29

Before versus after Aleinu: In the event that the Bris is taking place immediately after the morning prayers, then it is to be done before the prayer of Aleinu. [Shach 265 end; Maharil Hilchos Mila; Levush 265] However, practically, today this is no longer the custom and rather it is done after the Davening is complete. [Aruch Hashulchan 265 end] Hence, Aleinu Leshabeiach is recited at the end of Shacharis, as usually done, and then again after the Bris. [Bris Avos 3:16; See Os Shalom 265:39; Koreis Habris ; Shevach Habris 18 footnote 36]

If Mohel did not yet Daven: See Pesakim Uteshuvos 262:5 footnotes 30-32

Shabbos and Yom Tov: Custom is to do after Musaf. [See Pesakim Uteshuvos 262:5 footnote 33]

Rosh Hashanah: After the Torah reading, before the blowing of the Shofar, if taking place in Shul. [See Admur 584:9; Michaber 584:4; Pesakim Uteshuvos 262:5 footnotes 35-36]

Purim: After the Torah reading, before the Megillah reading, if taking place in Shul. [See M”A 687:5; Opinion in Terumas Hadeshen 266; 4; Chayeh Adam 154:6 brought in M”B 687:9; Pesakim Uteshuvos 262:5 footnote 8]

[4] Poskim in Pesakim Uteshuvos ibid footnote 12 and 19-21; Rav Groner in name of Rebbe, brought in Shevach Habris ibid footnote 12, that the Rebbe was very particular that the circumcision be scheduled for prior to midday and that even if for whatever reason it had to take place after midday, the invitation should state a time prior to midday, and that if it gets delayed then it gets delayed.

[5] Poskim in Pesakim Uteshuvos 262:4 footnote 22

[6] Igros Kodesh 4:154, brought in Shulchan Menachem 5:112; See Poskim in Pesakim Uteshuvos ibid footnote 10

Other opinions: Some Poskim rule that the aspect of Zerizin Makdimim Lemitzvos is of greater importance than Berov Am Hadras Melech, and overrides it and hence the circumcision should always take place in the morning. [Sdei Chemed Zayin Kelal 3; Pesakim Uteshuvos ibid footnote 15-17]

Opinion of Admur: See Admur 25:4 that Zerizin Makdimim overrules delayed Hiddur, although in 94:5 writes that later Hiddur overrides Zerizin Makdimim; See Likkutei Sichos 19 p. 76 in footnote 73 that both rulings are correct, as in 25:4 it discusses an external Hiddur of preceding the Tallis which is Tadir, and in 94:5 it discusses a Hiddur in the actual Mitzvah; See Poskim in Pesakim Uteshuvos ibid footnote 10

[7] See Igros Kodesh that the Rebbe offered a mere Limud Zechus, and not an actual directive