Short answer: It depends on your relationship with God

For example the same man could be addressed:

• as "Mr. Smith", which implies a professional relationship in for example a business or legal environment
• as "Johnathan", which implies he is known personally, perhaps by colleagues, classmates, and so on
• as "Jo", which might be a nickname or a shortened name given by close friends of family members
• as "Daddy", which implies an intimate relationship by his children
• as "Honey", which implies an intimate relationship by his wife

... and so.

Addressing God

O God

A formal way to address God, for example see the prayer by a repenting believer who has no intimate relationship with God yet:

But the tax collector stood at a distance and dared not even lift his eyes to heaven as he prayed. Instead, he beat his chest in sorrow, saying,

"O God, be merciful to me, for I am a sinner."

-- Luke 18:13 (NLT)

Lord

The believers in Acts who were not filled by the Holy Spirit yet, address God as "Lord":

They raised their voice to God with one accord and said:

“Lord, You are God, who made heaven and earth and the sea, and all that is in them, ... ... For truly against Your holy Servant Jesus, whom You anointed ... ... Now, Lord, look on their threats, and grant to Your servants that with all boldness they may speak Your word, by stretching out Your hand to heal, and that signs and wonders may be done through the name of Your holy Servant Jesus.”

And when they had prayed, the place where they were assembled together was shaken; and they were all filled with the Holy Spirit, and they spoke the word of God with boldness.

-- Acts 4:23-31 (NKJV)

Yahweh

אָ֣ז הוּחַ֔ל לִקְרֹ֖א בְּשֵׁ֥ם יְהוָֽה׃

Which directly translates to:

Then [men] began to call on the name of YHWH. -- BibleHub

The name, יְהוָ֖ה, directly translates to the Tetragrammaton YHWH. Because the vocals are uncertain some would pronounce it as "Jehovah" ("J" pronounced as a "y") by substituting the vowel marks for "Adonai" and putting them under the letters of יְהוָ֖ה. Others argue that "Jehovah" is incorrect because the vowels for Adonai are reversed, so they pronounced it "Yahoveh" or "Yahweh" or just "Yah". Some argue "Yahweh" is also incorrect because Hebrew lacks the English "w" sound. The Jewish tradition is to not pronounce the sacred name at all. Therefore, some substitute the word "Adonai" which means "my Lord" in its place.

Most modern English bible translations translate this name to GOD or LORD in capital letters to differentiate between the actual word "god" or "lord". Unfortunately some bible translations even drop the capitalization which removes God's name completely.

Abba Father

However, Jesus himself who has the most intimate relationship with God, addressed God as:

"Abba, Father, all things are possible for You." -- Mark 14:36 (NKJV)

According to Strong's Concordance:

Original Word:     Ἀββᾶ
Part of Speech:    Proper Noun, Indeclinable
Transliteration:   Abba
Phonetic Spelling: (ab-bah')
Definition:        Abba, father
Usage:             Abba, Father

As you can see the word "Abba" is the original Greek word that was not translated.

Abbá – "Father," also used as the term of tender endearment by a beloved child – i.e. in an affectionate, dependent relationship with their father; "daddy," "papa."

Given the above description of the Greek word "Abba" we can then understand that when the bible translators, translated Jesus' words as:

Therefor we can conclude that Jesus actually meant:

"Papa, all things are possible for You." -- Mark 14:36 (NKJV)

Now, when Paul says, that we too, may also have that kind of relationship with God:

But when the fullness of the time had come, God sent forth His Son, born of a woman, born under the law, to redeem those who were under the law, that we might receive the adoption as sons. And because you are sons, God has sent forth the Spirit of His Son into your hearts, crying out,

"Abba, Father!" (or simply "Papa" or "Dad")

Therefore, you are no longer a slave but a son, and if a son, then an heir of God through Christ.

-- Galatians 4:4-7 (NKJV)

and again in:

For as many as are led by the Spirit of God, these are sons of God. For you did not receive the spirit of bondage again to fear, but you received the Spirit of adoption by whom we cry out,

"Abba, Father." (or simply "Papa" or "Dad")

The Spirit Himself bears witness with our spirit that we are children of God.

-- Romans 8:14-16 (NKJV)

When the believers asked Jesus how to pray, his answer was:

When you pray, ... pray to your Father who is in the secret place; and your Father who sees in secret will reward you openly -- Matthew 6:6 (NKJV)

Jesus could have said "my Father", but instead Jesus said "your Father" or in Jesus' example prayer he addressed God as "Our Father":

In this manner, therefore, pray: Our Father in heaven, Hallowed be Your NAME. -- Matthew 6:9 (NKJV)

Note that Jesus said "in this manner", not "recite after me".

By saying this, it reveals that this prayer is meant to be a way in which we pray, not a word for word prayer that we vainly recite. Because remember, Jesus just told us a few verses ago that we shouldn’t pray with vain repetitions. -- The Biblical Foundation

Each prayer is intended to be a unique conversation with God.

Addressing Jesus

Jesus Himself said:

... in that day you will ask Me nothing. Most assuredly, I say to you, whatever you ask the Father in My name He will give you. -- John 16:23 (NKJV)

This implies that "the Father" is the provider, but Jesus is our High Priest (Mediator) through whom we have access to "the Father".

However, when Stephen was busy dying, he cried out:

"Lord Jesus, receive my spirit."

Then he fell on his knees and cried out,

"Lord, do not hold this sin against them."

When he had said this, he fell asleep.

-- Acts 7:59-60 (NIV)