Who exactly was included in the census?
Rashi (Shir ha'Shirim 3:7), Seforno, Ramban (26:64, based on Bava Basra, 121b), Bamidbar Rabah 5:2: It incorporated conscripts between the ages of 20 and 60, as men over the age of 60 did not go to war. 1
Tosfos (Bava Basra 117b DH mi'Kan): Even men over the age of 60 were included.
Abarvenel: The Torah did not say 'until 60', for some men above 60 are able to fight.
If it was necessary to count the tribes as is the way of kings who order a census, why did Hashem instruct Moshe and Aharon to find out the sum total of the entire nation?
Ramban #1: So that the people should be aware of Hashem's great kindness, inasmuch as, when they arrived in Egypt they numbered seventy, and now, they were numerous like the sand of the sea, so many from the age of 20 and upwards. 1
Ramban #2: It was in order that every person would be able to pass before Moshe and Aharon, who would gaze upon them with an Ayin Tovah and bestow upon them a Berachah - "Hashem Elokei Avoseichem Yosef aleichem kachem Elef Pe'amim" (Devarim 1:11), and you will not be reduced, and the half-Shekel would atone for them.
Ramban #3: Because they were poised to enter Eretz Yisrael, to begin the conquest of Kena'an, 2 and as is the way of an army going into battle, 3 Moshe and the Nesi'im needed to count the soldiers, to know the sum total of fighting men and how many there were in each tribe. 4
Ramban #4: Because they were also about to distribute the land, and it was necessary to know the numbers, in order to know into how many portions they would need to divide the land.
Not even counting the women and children.
Ramban: Which is what the Torah is referring to when it wrote (in Pasuk 3) "Kol Yotzei Tzava b'Yisrael".
Ramban: So that when they arrived at the Plains of Mo'av, they would be able to present them with their battle orders, since the Torah does not rely on miracles.