1) One should don the tallit before donning the tefillin, due to the halachic principle of מעלין בקודש ואין מורידין — “One ascends in sanctity, and does not descend.” Wearing tefillin is a more sacred act than wearing a tallit, because whereas with a tallit one covers himself with a mitzvah garment, by wearing tefillin one binds his body to the realm of kedushah (sanctity). It is thus proper to first don the tallit and then “ascend in sanctity” by donning tefillin.[6]

2) If one has tefillin but not a tallit, and he expects to receive a tallit before the final time for Shema, then he should not don his tefillin until after he receives the tallit. If, however, he suspects that the tallit will arrive only after the final time for Shema, then he should put on his tefillin even without the tallit, so that he can recite Shema and the Amidah with tefillin. Of course, once the tallit arrives he should don the tallit, as well.[7]