Gemara

(Rabah bar bar Chanah): Forty Se'ah of Tefilin were found on the heads of the victims in Beitar.

(R. Yanai b'Rebbi Yishmael): Three crates were found. Each held 40 Se'ah.

(Beraisa): 40 crates were found, each holding three Se'ah.

All agree that they found 40 Se'ah of Tefilin Shel Yad (of the hand) and 120 Se'ah of Shel Rosh (of the head).

Menachos 36a (Beraisa): One puts on the Shel Yad before the Shel Rosh. When removing them, he removes the Shel Rosh before the Shel Yad.

Question: We understand the first law - "u'Kshartam l'Os Al Yadecha (and then) v'Hayu l'Totafos Bein Einecha";

Why must one remove the Shel Rosh first?

Answer (Rabah): "V'Hayu (plural) l'Totafos Bein Einecha" - whenever Tefilin are on your head, you are wearing both.

Yoma 33b (Rava): Reish Lakish taught that Dishun (removing the ashes) of the Mizbe'ach precedes Dishun ha'Menorah because we do not pass over Mitzvos. We learn from this that one may not pass over the arm for the head Tefilin

Question: What should he do?

Answer: He goes from the hand to the head.

Rishonim

Rashi (58a DH d'Dar'a): There was a larger volume of head Tefilin because each one has four compartments. There was not four times as much as the hand Tefilin, because the one box of hand Tefilin is bigger than one compartment of head Tefilin.

Rebuttal (Etz Yosef citing R. Akiva Eiger, and Rashash): We concluded that there were 40 Sa'im on the heads, and more Shel Yad! Also, our custom is that the hand and head Tefilin are the same size! Rather, one puts on the Shel Yad first, and removes it last. There are three situations: one is putting on Tefilin, wearing both of them, or removing Tefilin. At all three times people are wearing the Shel Yad, but only in the middle case they wear the Shel Rosh. This is why there were three times as many Shel Rosh as Shel Yad.

Note: This is reasonable if we assume that everyone wore Tefilin only a short time, e.g. due to the invaders.

Rif and Rosh (Hilchos Tefilin (after Menachos) 8b and Siman 15): One puts on the Shel Yad before the Shel Rosh, and removes the Shel Rosh before the Shel Yad. We learn from "u'Kshartam l'Os Al Yadecha v'Hayu l'Totafos Bein Einecha."

Nimukei Yosef (8b DH Ein): If one encountered the Shel Rosh before the Shel Yad, he puts on the Shel Rosh first (to avoid passing over Mitzvos), even though this is improper.

Rambam (Hilchos Tefilin 4:8): When removing Tefilin, one should not put the Shel Rosh in the Kli on top of the Shel Yad, for then the next time he puts on Tefilin, he will encounter the Shel Rosh first. He will need to put it aside, for we put on the Shel Yad before the Shel Rosh. One may not leave aside a Mitzvah and go to do another Mitzvah. Rather, he must do the first Mitzvah that comes to him. Therefore, he puts the Shel Yad in the Keli last, on top of the Shel Rosh, so the next time he will encounter it first.

Rosh (ibid.): Rashi (Yoma 33b DH Avorei) says that Rava learned from Reish Lakish that one may not put on the Shel Rosh first, for his arm encounters the Tefilin before his head. This is difficult. A verse teaches this - "u'Kshartam l'Os Al Yadecha v'Hayu l'Totafos Bein Einecha"! R. Tam says that Rava discusses removing Tefilin and putting them in a pouch. He forbids to put the Shel Yad in first (and later the Shel Rosh on top of it), for then the next time he puts on Tefilin he will encounter the Shel Rosh first, and he will need to pass over it to put on the Shel Yad first!

Tosfos (Erchin 3a DH v'Shel Yad) "V'Hayu l'Totafos Bein Einecha" teaches that when one will wear both Tefilin, he must put on the Shel Yad first.

Poskim

Shulchan Aruch (OC 25:11): Some forbid removing the Shel Rosh from the bag until the Shel Yad is on.

Beis Yosef (DH Yesh): Some take out the Shel Rosh before the Shel Yad is on, to get it ready and minimize the delay. This is wrong, for they pass over Mitzvos! Whatever is done to put it on is not an interruption. According to Kabalah, one should not remove the Shel Rosh until the Shel Yad is on.

Mishnah Berurah (39): One may not take out Shel Rosh by itself before the Shel Yad is on, due to passing over Mitzvos. This is not a problem if he takes them out of the bag together, but Kabalah warns against even this.

Rema: Even if both are in front of him, outside the bag, he should not untie the Shel Rosh before the Shel Yad is on.

Magen Avraham (19): Once he takes it in his hand and does not put it on, he passes over the Mitzvah.

Shulchan Aruch (28:2): One removes the Shel Rosh first, due to "v'Hayu l'Totafos Bein Einecha." One removes the Shel Rosh while standing and puts it in the bag. He puts the Shel Yad over it, so the next time he puts on Tefilin, he will encounter the Shel Yad first.

Beis Yosef (DH v'Yani'ach): If one took out his Shel Rosh before the Shel Yad, he must put it aside and put the Shel Yad on first (Rambam and Rosh). The order specified by the Torah overrides passing over Mitzvos. The Nimukei Yosef disagrees; his is the minority opinion.

Mishnah Berurah (28:7,8): The Bach and Taz say that the Tefilin bag should be long and narrow, so the Shel Rosh will be over the Shel Yad. The custom follows the Magen Avraham, who says that it is better for them to be side by side. The Shel Rosh should be on the right so one will encounter it first. One should not take off the Shel Yad until he puts away the Shel Rosh, lest he put the Shel Yad in the bag first.

Kaf ha'Chayim (14,15): One should be consistent to always put the Shel Rosh on the right, or always on the left, so it will be habit and he will never take it out first. The Shel Yad should not be on top of the Shel Rosh, for the Shel Rosh is more Kodesh. Similarly, a Talis or Sidur should not rest on top of Tefilin.

Kaf ha'Chayim (26:1): If one put on the Shel Rosh first, Mahari Molcho (85) says that he was Yotzei. The Avudraham says that the Gemara says that they are Me'akev each other to teach that if he changed the order, he was not Yotzei. One opinion in the Yerushalmi says that this is an Aveirah that prevents one from saying in Viduy Ma'aser "I did all Your Mitzvos ... I did not transgress." This does not show that he was not Yotzei!