Repentance Before Asking
It's recommended to express repentance when asking Allāh for your needs; because it may be that a person has a sin preventing his supplication from being accepted.
Allāh the Most High says,
ثُمَّ اَنَابَ ◌ قَالَ رَبِّ اغۡفِرۡ لِىۡ وَهَبۡ لِىۡ مُلۡكًا لَّا يَنۡۢبَغِىۡ لِاَحَدٍ مِّنۡۢ بَعۡدِىۡۚ
"He turned to Us and prayed: ‘Lord forgive me! Grant me such power as no one after me will have..." (Sūrah Ṣād (38): 34-35)
وَاَصۡلِحۡ لِىۡ فِىۡ ذُرِّيَّتِىۡ ؕۚ اِنِّىۡ تُبۡتُ اِلَيۡكَ
"...And instil righteousness in my offspring. I truly repent to You...” (Sūrah Al-Aḥqāf (46): 15)
From the best of supplications, is to ask Allāh for pardon and well-being; because pardon secures the hereafter and well-being secures this life.
From the reasons of getting supplications accepted is the re-affirmation of (Allāh's) oneness and admittance of the soul's transgression.
Allāh the Most High says,
فَنَادٰى فِى الظُّلُمٰتِ اَنۡ لَّاۤ اِلٰهَ اِلَّاۤ اَنۡتَ سُبۡحٰنَكَ إِنِّي كُنتُ مِنَ الظَّالِمِينَ
"Then in the (veils of) darkness he cried out, 'There is no deity worthy of worship except You. Glory be to You! I have certainly done wrong.'" (Sūrah Anbiyā’ (21): 87)