The Sandak – the individual given the privilege of holding the infant during a Berit Mila – has been compared to a Kohen in the Bet Ha’mikdash bringing the Ketoret (incense offering), which was considered an especially precious Misva. As such, there are various blessings and rewards associated with the Misva of serving as Sandak. Thus, for example, just as a Kohen who brought the Ketoret in the Bet Ha’mikdash was blessed with wealth, similarly, serving as Sandak brings financial blessing.
The work Berit Abot mentions that since the Sandak is compared to the Kohen offering the Ketoret on the altar, he should be proactive in taking the child from the father. If the father simply places the infant on the Sandak’s lap, the Sandak has not actively participated in the Berit in any way, and he thus cannot be compared to a Kohen bringing an offering. Therefore, the Sandak should take the baby with his hands from the father and then place the baby on his lap.
The Rama (Rav Moshe Isserles of Cracow, 1530-1572), in Yoreh De’a (265:11), addresses the case of a Berit that takes place on Monday or Thursday, when the Torah is read, and the father, the Mohel and the Sandak are all present in the synagogue. If all three are either a Kohen, a Levi or a Yisrael, such that only one of them can be given an Aliya, then, the Rama rules, the Aliya should be given to the Sandak. The work Zocher Ha’berit explains that the father and Mohel both have an obligation vis-à-vis the Berit – the father is obligated to ensure his child is circumcised, and the Mohel is obligated to perform the circumcision – whereas the Sandak bears no obligation at all. Since his Misva is done purely voluntarily, he earns the right to receive the Aliya.
The Kabbalists teach that the Sandak has the ability to transform the prosecuting angels, who advocate against the Jewish People before G-d, into defending angels, who advocate on our behalf. And thus the word "Sandak" may be read as an acrostic for the phrase, "Sanegor Naasa Din Kategor" – the prosecutor in judgment becomes an advocate.
Summary: Serving as Sandak – holding the baby during the Berit – is considered a great privilege and wields great rewards. When the father gives the baby to the Sandak, the Sandak should preferably take the baby with his hands and put it on his lap, rather than remaining passive as the father places the baby on his lap. If the Torah is read on the day of a Berit and there is only one Aliya available for the father, the Mohel and the Sandak, it should be given to the Sandak.