The Rebbe taught that one should daven early in the morning to the best of one’s ability.
(Sichos ha-Ran 31. Cf. Alim Le-terufah 26. This was the prevailing attitude during the first generations of the Chassidic movement; e.g., see Tzava’as ha-Rivash 16, regarding the Baal Shem Tov, and Imrei Pinchas 389, regarding Rabbi Pinchas of Koretz. In general, the Rebbe encouraged us to not postpone davenning, but to attend to all the tefillos as soon as possible.)
The Rebbe held that because of the greatness of tefillah, one should daven all tefillos promptly. One never knows what obstacles might deter him later.
(Si’ach Sarfey Kodesh II, 172; accordingly, Breslover Chassidim try to daven Minchah before the shekiah.)
The Rebbe did not approve of drinking coffee or tea before shacharis. He personally did not even drink water before praying in the morning. This has become common practice among Breslover Chassidim.
(Sichos ha-Ran 277; Si’ach Sarfey Kodesh IV, 504; cf. Zohar II, 215b, III, 141b; Shulchan Arukh, Orach Chaim 89:3, 4; Be’er Heitiv, Orach Chaim 89:11; also Si’ach Sarfey Kodesh II, 1-57, in the name of the Baal Shem Tov. Nevertheless, Reb Noson acknowledges that drinking water is permitted according to halakhah; see Likkutei Halakhos, Birkos ha-Shachar 3:5. According to most authorities, even tea or coffee is permitted if one is weak. Certainly this applies to a person with health problems, who is even permitted to eat, as stated in Shulchan Arukh, ad locum.)
The Rebbe stated that one should not be overly concerned with the requirement to go to the bathroom before davenning, but one may rely upon the ruling of the RIF (based on Berakhos 14b) that it is enough if one feels capable of walking one parsah (a little less than a mile) without attending one’s needs. Thus, one will not delay his prayer unnecessarily.
(Sichos ha-Ran 30; Chayei Moharan 52; cf. Shulchan Arukh, Orach Chaim 92)
He also said of certain Chassidic leaders of his day, “The tzaddikim are making a mistake by praying after the z’man tefillah.”
(Chayei Moharan 487; Shulchan Arukh, Orach Chaim 89:1. Many of these Chassidic masters made lengthy spiritual and physical preparations and then davenned at great length, causing them to miss the z’man tefillah. Therefore, this applies all the more so to those of us who may delayed by oversleeping or by procrastinating before coming to shul.)