Barukh She'amar

ואומר ברוך שאמר והיה העולם. לשון חכמים הוא שאומר במקומות הרבה גלוי וידוע לפני מי שאמר והיה העולם והוא על שם כי הוא אמר ויהי, ור"ל שעל ידי אמירה נברא העולם בלא שום יגיעה ולא שום פעולה אחרת שנא' בדבר ה' שמים נעשו.

והיינו דאמרינן בבראשית רבה שהעולם הזה נברא בה"א שנא' אלה תולדות השמים והארץ בהבראם בהא בראם. והטעם כמו הה"א שאין בכל האותיות יותר קלה ממנה להאמר בפה כך ברא העולם בלא יגיעה ועמל.

Then, we say "Blessed is the One Who Spoke and the World Was." This is language of the sages who say in many places "revealed and known before the One Who Spoke and the World Was, in the name of "For G-d spoke and it was" (Psalms 33:9). This is to say that through speech the world was created without any struggle or any other action, as it says "with the word of G-d the heavens were made" (Psalms 33:6).

This parallels what we say in Bereishit Rabbah that the world was created with a "heh" as it says "these are thte generations of the heavens and the earth in their formation" - with "heh" G-d created them. The purpose of this is that just as "heh" is the easisest of all the letters to pronounce in the mouth, so did G-d create the world without struggle or intensive labor.

ברוך שאמר וכו' צריך לאומרו בניגון ובנעימה כי הוא שיר נאה ונחמד וכתב בספר היכלות שיש בו פ"ז תיבות וסי' ראשו כתם פז וכן הוא נוסח אשכנזים

ונתקנה ברכה זו משום הא דאיתא בפרק כל כתבי יהא חלקי עם גומרי הלל בכל יום ומסקינן כי קאמר בפסוקי דזמרה ומאי ניהו תהלה לדוד עד כל הנשמה תהלל יה

ותו גרסינן בפ"ק דברכות (ד:) א"ר אלעזר כל האומר תהלה לדוד בכל יום ג"פ מובטח לו שהוא בן העוה"ב וכן דרש ר' שמלאי לעולם יסדר אדם שבחו של מקום ואחרי כן יתפלל לכן תקנו לאומרם קודם תפלה וקבעו ברכה זו לפניהם ואחת לאחריהם והיא ישתבח

Barukh She'amar and the rest... Needs to be said with melody and pleasantness, because it is a beautiful and sweet poem. It is written in the Sefer Heikhalot that there are 87 (paz) letters and this signifies "his head is the finest golden treasure, his locks curled and raven-colored" (Song of Songs 5:11) and this is the standard Askhenazic rite.

This blessing was instituted because of what is brought in the Talmud Bavli Shabbat chapter 16 "All holy writings should be saved from a fire": May my share be among those who complete Hallel every day and we conclude that this means Pesukei D'Zimra. And what is that? "Tehillah l'David" until "Kol HaNeshamah Tehallel Yah"

Furthermore, we repeat in the first chapter of Berakhot that Rabbi Elazar said "everyone who says "Tehillah l'David" three times a day, it is assured that they are a child of the world to come." Rabbi Simlai interpreted similarly "a person should always arrange their praise of the Presence and then afterwards, pray."

This is why the sages instituted the saying of psalms before prayer and formulated this blessing before them and another blessing afterwards which is Yishtabach.

אָמַר רַבִּי יוֹסֵי: יְהֵא חֶלְקִי מֵאוֹכְלֵי שָׁלֹשׁ סְעוּדוֹת בַּשַּׁבָּת. אָמַר רַבִּי יוֹסֵי: יְהֵא חֶלְקִי מִגּוֹמְרֵי הַלֵּל בְּכׇל יוֹם. אִינִי?! וְהָאָמַר מָר: הַקּוֹרֵא הַלֵּל בְּכׇל יוֹם הֲרֵי זֶה מְחָרֵף וּמְגַדֵּף! כִּי קָאָמְרִינַן — בִּפְסוּקֵי דְזִמְרָא.
Rabbi Yosei said: May my portion be among those who eat three meals on Shabbat. Apropos this statement of Rabbi Yosei, the Gemara cites additional declarations. Rabbi Yosei said: May my portion be among those who complete hallel every day. The Gemara is surprised at this: Is that so? Didn’t the Master say: One who reads hallel every day is tantamount to one who curses and blasphemes God. He displays contempt for hallel by not reserving it for days on which miracles occurred. The Gemara answers: When we say this statement of Rabbi Yosei, we are referring to the verses of praise [pesukei dezimra], recited during the morning service, not to hallel (Psalms 113–118) recited on special days.
אָמַר רַבִּי אֶלְעָזָר, אָמַר רַבִּי אֲבִינָא: כָּל הָאוֹמֵר ״תְּהִלָּה לְדָוִד״ בְּכָל יוֹם שָׁלֹשׁ פְּעָמִים — מוּבְטָח לוֹ שֶׁהוּא בֶּן הָעוֹלָם הַבָּא. מַאי טַעְמָא? אִילֵּימָא מִשּׁוּם דְּאָתְיָא בְּאָלֶף בֵּית, נֵימָא ״אַשְׁרֵי תְמִימֵי דָרֶךְ״ דְּאָתְיָא בִּתְמָנְיָא אַפִּין. אֶלָּא מִשּׁוּם דְּאִית בֵּיהּ ״פּוֹתֵחַ אֶת יָדֶךָ״, נֵימָא ״הַלֵּל הַגָּדוֹל״ דִּכְתִיב בֵּיהּ ״נֹתֵן לֶחֶם לְכָל בָּשָׂר״. אֶלָּא מִשּׁוּם דְּאִית בֵּיהּ תַּרְתֵּי.
Tangential to Rabbi Yoḥanan’s statement that one who juxtaposes redemption and prayer is assured of a place in the World-to-Come, a similar statement is cited. Rabbi Elazar said that Rabbi Avina said: Anyone who recites: “A Psalm of David” (Psalms 145) three times every day is assured of a place in the World-to-Come. This statement extolling the significance of this particular chapter of Psalms, usually referred to as ashrei because its recitation is preceded by recitation of the verse, “Happy [ashrei] are those who dwell in Your House, they praise You Selah” (Psalms 84:5), raises the question: What is the reason that such significance is ascribed to this particular chapter? If you say that it is because it is arranged alphabetically, then let us say: “Happy are they who are upright in the way” (Psalms 119) where the alphabetical arrangement appears eight times. Rather, if you suggest that this particular chapter is recited because it contains praise for God’s provision of sustenance to all of creation: “You open Your hand and satisfy every living thing with favor” (Psalms 145:16), then let him recite the great hallel (Psalms 136), in which numerous praises are written, including: “Who provides food to all flesh, Whose kindness endures forever” (Psalms 136:25). Rather, the reason why tehilla leDavid is accorded preference is because it contains both an alphabetic acrostic as well as mention of God’s provision of sustenance to all creation.