THE PROPER ORDER TO PUT ON TEFILIN [Tefilin:Hanachah]
Rava: Dishun of the Mizbe'ach precedes Dishun ha'Menorah because Reish Lakish's teaching, that we do not pass over Mitzvos. When one enters the Heichal, he encounters the Mizbe'ach before the Menorah.
Rava: We learn from Reish Lakish that it is forbidden to pass over the arm for the head Tefilin (alternatively - to pass the arm Tefilin over the head Tefilin).
Question: What should he do?
Answer: He goes from the hand to the head.
Rashi (DH Avorei): Rava forbids to put on the Shel Rosh first, for his arm encounters the Tefilin before his head. The answer is that one must put the Shel Yad on first.
Tosfos (DH Avorei): The Torah mandates donning Shel Yad first - "U'Kshartam l'Os Al Yadecha v'Hayu l'Totafos Bein Einecha"! Rather, 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 have to pass over it to put on the Shel Yad first! R. Eliyahu says that he discusses which Tefilin one should touch first when touching them.
Rambam (Hilchos Tefilin 4:8): When one removes his Tefilin and puts them in a Keli, he should not put the Shel Rosh on top of the Shel Yad, for then the next time he puts on Tefilin, he will encounter Shel Rosh first and he will have to put it aside to put the Shel Yad on first, for we do not put on Shel Rosh before Shel Yad. It is forbidden to 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 Shel Yad first.
Shulchan Aruch (OC 25:1): After putting on a Talis with Tzitzis he puts on Tefilin, for we ascend in Kedushah. If one puts his Talis and Tefilin in the same bag, he should not put the Tefilin on top, lest (next time) he encounter the Tefilin first and he will have to put them on first, to avoid passing over the Mitzvah.
Nimukei Yosef (Hilchos Tzitzis (printed after Menachos) 12a DH Nahagu): We put on Tzitzis first because Tzitzis are equated to all the Mitzvos. Also, Tzitzis applies even on Shabbos and Yom Tov, so it is more Tadir than Tefilin. Sefer ha'Yir'ah also says so.
Rebuttal (Sha'agas Aryeh 28): Most Poskim hold that Tzitzis does not apply at night. Most Poskim hold that Tefilin applies at night, just Chachamim decreed against this lest one sleep in them. This decree does not remove the mid'Oraisa attribute of Tadir. Even if Tefilin does not apply on Shabbos, since it applies day and night it is more Tadir than Tzitzis. And even if the Halachah would follow the opinion that mid'Oraisa Tzitzis applies at night and Tefilin does not, so Tzitzis is Tadir, since Tefilin is a matter of Kedushah, one may fulfill it first. Further, it seems that Tzitzis cannot be considered Tadir, for it is not obligatory; one need not wear a four-cornered garment.
Nimukei Yosef (ibid.): However, if one wears a Talis Gadol over all his garments including the Maktoren (a hooded robe) on his head, he encounters Tefilin first and should out it on first, for we do not pass over Mitzvos.
Question (Beis Yosef DH v'Acher): Putting on all one's garments including the Maktoren on his head does not necessitate encountering Tefilin first!
Answer (Darchei Moshe 1): Tefilin are placed (directly) on the arm, before his garment.
Beis Yosef (ibid.): Sefer ha'Yir'ah says to put on Talis Katan before Tefilin, and a Talis Gadol after Tefilin. The Agur cites the Zohar to say that is a great Isur to put Tefilin on before Tzitzis. Mekubalim of Sefard say that one who has no Talis Katan should certainly put on a Talis Gadol before Tefilin to fulfill the Zohar. It is best to put on a Talis Katan, then Tefilin, and then a Talis Gadol.
If one took out his Tefilin Shel Rosh before Shel Yad, he must put it aside and put the Shel Yad on first. The order specified by the Torah overrides passing over Mitzvos. The Nimukei Yosef disagrees, but his is the minority opinion. However, if one took out Tefilin before his Talis, he must put Tefilin on first. Not passing over Mitzvos overrides an Asmachta that Talis should be first.
Question (Magen Avraham 1): If the Tefilin are in a bag, passing over Mitzvos should not apply! The Shulchan Aruch itself says not to take the Tefilin Shel Rosh out of the bag until the Shel Yad is properly placed!
Mishnah Berurah (1): He should put on the Talis first even if it is only obligated mid'Rabanan, e.g. it is borrowed.
Mishnah Berurah (3): Even if he did not touch the Tefilin, if they are closer when he sticks out his hand he must put them on first. This is only if he wants to put them on now. If he does not intend to put them on until later, passing over Mitzvos does not apply.
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 remove 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): 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.
Rema: If Tefilin are available but not Tzitzis, he need not wait for Tzitzis. He puts on the Tefilin, and when the Talis comes he puts it on.
Mishnah Berurah (Sof Siman 34): If one removed the bag with R. Tam Tefilin first, he puts them aside because we hold that Rashi Tefilin are primary. L'Chatchilah, one should ensure that this does not happen.