Expand how we can follow in the footsteps of Prophet Muhammad (ﷺ). Provide more references to the hadiths that mention the dhikr below, Insha-Allah it will help further your understanding and reinforce you to develop a new prayer habit.
There are many hadiths regarding the barakah for the person who recites bismillah (e.g, before eating, leaving the house). Recommended before starting any deed, it is a dhikr of rememberance of Allah.
Abu al-Malih reported on the authority of a man: I was riding on a mount behind the Prophet (ﷺ). It stumbled. Thereupon I said: May the devil perish! He said: do not say; may the devil perish! For you say that, he will swell so much so that he will be like a house, and say: by my power. But say: in the name of Allah; for when you say that, he will diminish so much so that he will be like a fly. (Sahih Al-Albani - Sunan Abi Dawud 4982)
Anas bin Malik narrated that: Umm Sulaim came upon the Prophet (ﷺ) and said: "Teach me some words that I can say in my Salat." So he said: "Mention Allah's Greatness (saying: Allahu Akbar) ten times, mention Allah's Glory (saying: Subhan Allah) ten times, and mention Allah's praise (saying: Al-Hamdulilah) ten times. Then ask as you like, (for which) He says: 'Yes. Yes.'" (Sahih Darussalam - Jami at-Tirmidhi 481)
On the authority of Abu Malik al-Harith bin Asim al-Ashari (may Allah be pleased with him) who said: The Messenger of Allah (ﷺ) said: "Purity is half of Iman. Alhamdulillah (praise be to Allah) fills the scales, and subhan-Allah (how far from imperfection is Allah) and Alhamdulillah (praise be to Allah) fill that which is between heaven and earth. And the Salah (prayer) is a light, and charity is a proof, and patience is illumination, and the Qur'an is a proof either for you or against you. Every person starts his day as a vendor of his soul, either freeing it or bringing about its ruin." (Sahih Muslim 223)
Narrated Jabir bin `Abdullah: Whenever we went up a place we would say, "Allahu-Akbar (ie Allah is Greater)", and whenever we went down a place we would say, "Subhan-Allah." (Sahih al-Bukhari 2993)
On the virtue of those who praise Allah (سُبْحَٰنَهُۥ وَتَعَٰلَىٰ). This dhikr also affirms Allah's oneness, a concept known as Tawhid, a central tenet of Islam. Jabir bin 'Abdullah said:"I heard the Messenger of Allah (ﷺ) say: 'The best of remembrance is La ilaha illallah (None has the right to be worshiped but Allah), and the best of supplication is Al-Hamdu Lillah (praise is to Allah). '" (Hasan Darussalam - Sunan Ibn Majah 3800)
On the virtue of those who praise Allah (سُبْحَٰنَهُۥ وَتَعَٰلَىٰ). This dhikr also affirms Allah's oneness, a concept known as Tawhid, a central tenet of Islam. Jabir bin 'Abdullah said:"I heard the Messenger of Allah (ﷺ) say: 'The best of remembrance is La ilaha illallah (None has the right to be worshiped but Allah), and the best of supplication is Al-Hamdu Lillah (praise is to Allah). '" (Hasan Darussalam - Sunan Ibn Majah 3800)
Imam Al-Auza'i (one of the subnarrators) of this Hadith was asked: "How forgiveness should be sought?" He replied: "I say: Astaghfirullah, Astaghfirullah (I seek forgiveness from Allah. I seek forgiveness from Allah)." (Sahih al-Bukhari 6405)
Abu Hurairah (ra) reported: The Messenger of Allah (ﷺ) said, "There are two statements that are light for the tongue to remember, heavy in the Scales and are dear to the Merciful: 'Subhan-Allahi wa bihamdihi, Subhan-Allahil-Azim [Glory be to Allah and His is the praise, (and) Allah, the Greatest is free from imperfection]'." (Sahih al-Bukhari 6682 & 6406)
Anas bin Malik said: “Whenever a matter would distress him, the Prophet (ﷺ) would say: ‘O Living, O Self-Sustaining Sustainer! In Your Mercy do I seek relief (Yā Ḥayyu yā Qayyūm, bi-raḥmatika astaghīth).’” And with this chain, that he said: “The Messenger of Allah (ﷺ) said: ‘Be constant with: “O Possessor of Majesty and Honor (Yā Dhal-Jalāli wal-Ikrām).’” (Hasan Darussalam - Jami` at-Tirmidhi 3524)
It was narrated from Abu Hurairah that: the Messenger of Allah (ﷺ) passed by him when he was planting a plant, and said: "O Abu Hurairah, what are you planting?" I said: "A plant for me." He said: "Shall I not tell you of a plant that is better than this?" He said: "Of course, O Messenger of Allah." He said: "Say: 'Subhan-Allah, wal-hamdu-lillah, wa la ilaha illallah, wa Allahu Akbar (Glory is to Allah, praise is to Allah, none has the right to be worshiped but Allah and Allah is the Most Great.)' For each one a tree will be planted for you in Paradise." (Sahih Al-Albani - Sunan Ibn Majah 3807)
It was narrated that Hazim bin Harmalah said: "I passed by the Prophet (saas) and he said to me: 'O Hazim, say often: "La hawla wa la quwwata illa billah (there is no power and no strength except with Allah)," for it is one of the treasures of Paradise.'" (Hasan Darussalam - Sunan Ibn Majah 3826)
Aishah (ra) reported: Prior to his demise, the Messenger of Allah (ﷺ) used to supplicate frequently: Subhan Allahi wa bihamdihi; Astaghfirullaha wa atubu ilaihi (Allah is free from imperfection, and I begin with praising Him. I beg forgiveness from Allah and I turn to Him in repentance)." (Riyad as-Salihin 1877)
Ibn Umar said: “In one sitting of the Messenger of Allah (peace be upon him), one could count that he said a hundred time, before he would get up: 'O my Lord, forgive me, and accept my repentance. Verily, You are the Oft-Returning, the Most Forgiving (Rabbighfirlī watub `alayya innaka antat-Tawwābul-Ghafūr).'” (Sahih Darussalam - Jami at-Tirmidhi 3434 - Riyad as-Salihin 1872)
Narrated from Ibn ‘Abbaas (may Allah be pleased with him) that the Prophet (blessings and peace of Allah be upon him) used to say between the two prostrations: “Allaahumma ighfir li warhamni wajburni wahdini warzuqni (O Allah, forgive me, have mercy on me, console me, guide me, and grant me provision).” (Sahih Al-Albani - Jami` at-Tirmidhi 284)
It was narrated that ‘Ubadah bin As-Samit said: “The Messenger of Allah (ﷺ) said: ‘Whoever wakes up in the morning and says upon waking: La ilaha illallah wahdahu la sharika lahu, lahul-mulku wa lahul-hamd, wa Huwa ‘ala kulli shay’in Qadir; Subhan-Allah walhamdu lillahi, wa la ilaha illallahu, wa Allahu Akbar, wa la hawla wa la quwwata illa billahil-‘Aliyil-‘Azim, then he supplicates Rabbighfirli (O Lord, forgive me), he will be forgiven.’” Walid said: “Or he said: then if he supplicated, it will be answered for him then if he stood up and performed ablution and then performed prayer, his prayer would be accepted. (Sahih Darussalam - Sunan Ibn Majah 3878)
Narrated `Abdur-Rahman bin Abi Laila: Ka`b bin Ujrah met me and said, "Shall I not give you a present I got from the Prophet?" `Abdur-Rahman said, "Yes, give it to me." I said, "We asked Allah's Messenger (ﷺ) saying, 'O Allah's Messenger (ﷺ)! How should one (ask Allah to) send blessings on you, the members of the family, for Allah has taught us how to salute you ( in the prayer)?' He replied with this supplication. (Sahih al-Bukhari 3370)