The Gemara starts with the question תנא היכא קאי דקתני מאימתי which loosely explained means, why does the Mishna start with "From when do we read the Shema" which already assumes that there is in fact a Mitzvah to read Shem? It should have started with the source for this Mitzvah? One can ask a more basic question, why does the first Mishna in Shas start with Shema? It is not the first mitzvah in the Torah. The gloss on Rambam's Introduction to his Commentary on Mishna explains that this is based on the idea ראשית חכמ יראת ה, the beginning of wisdom is fearing of G-d. Therefore Rav Yehudah Hanasi and his colleagues chose to begin Mishna with the most basic Mitzvah expressing our fear of G-d which is the Shema. This teaches us that an overarching theme of Berachot is the fear of G-d. Look for this as you learn through the tractate in both the Halakic and Aggadic sections.
The Gemara answers why we start with Shema at night and day and then switch the order to the Berachot of Shema of day followed the the Berachot of night with תנא פתח בערבית והדר תני בשחרית עד דקאי בשחרית פריש מילי דשחרית והדר פריש מילי דערבית, the Tanna started with the night [Shema] and then explained day [Shema]. While he was in the morning he then explained other things in the morning prayer [namely the morning Berachot of Shema] and then he went back to explaining the night again. This explanation could be due to a mnemonic reason for the structure of the Mishna. It could be an example of chiastic structure which in most basic form is characterized as ABBA. This structure would have been used since the Mishnayot were meant to be studied by rote and a chiastic structure which greatly improve oral retention of the material.
One final question on the second Amud. How come all of the examples the Gemara gives for Shema revolve around food? It uses the eating time of the Kohain, poor man, regular person on Shabbat, regular person on weekdays etc. I have no good answer for this and I welcome responses which you can provide in the comments section to this posting.