The occupation portrayed most favorably in the New Testament is...

First of all, God, Lord, Messiah, and Savior are not occupations, so don't go there.

Okay, fisherman is perhaps the obvious answer. So maybe I should have said "except fisherman" in the title, but the title was already too long. On the other hand, fishermen deny and abandon Jesus, so that occupation has some bad optics in the New Testament.

So, with the caveats of no Jesus as an answer, and (perhaps) not fisherman, What is next?

That, arguably, would be the occupation of Roman Centurion. They get a lot of good ink in the New Testament.

Before a recap of their favorable representation, what exactly was a centurion? According to wiki:

A centurion (/sɛnˈtjʊəriən/; Latin: centurio; Greek: κεντυρίων, kentyríōn or ἑκατόνταρχος, hekatóntarkhos) was a professional officer of the Roman army after the Marian reforms of 107 BC. Centurions commanded a century of around 80 legionaries. (Wikipedia)

What are the results of a search of the New Testament of centurion? Well, a centurion receives some of the most lavish praise recorded from the mouth of Jesus:

⁵ When he had entered Capernaum, a centurion came forward to him, appealing to him, ⁶ “Lord, my servant is lying paralyzed at home, suffering terribly.” ⁷ And he said to him, “I will come and heal him.” ⁸ But the centurion replied, “Lord, I am not worthy to have you come under my roof, but only say the word, and my servant will be healed. ⁹ For I too am a man under authority, with soldiers under me. And I say to one, ‘Go,’ and he goes, and to another, ‘Come,’ and he comes, and to my servant, ‘Do this,’ and he does it.” ¹⁰ When Jesus heard this, he marveled and said to those who followed him, “Truly, I tell you, with no one in Israel have I found such faith. (Matt 8:5-10)

The text continues with more (and powerful) indirect praise.

We encounter another unnamed centurion at the crucifixion:

³⁸ And the curtain of the temple was torn in two, from top to bottom. ³⁹ And when the centurion, who stood facing him, saw that in this way he breathed his last, he said, “Truly this man was the Son of God!” (Mark 15:38-39)

⁴⁷ Now when the centurion saw what had taken place, he praised God, saying, “Certainly this man was innocent!” (Luke 23:47)

When it is time for the gospel to go to the Gentiles in an official sense, who was it that God would choose to receive the honor? It was Cornelius, a centurion:

At Caesarea there was a man named Cornelius, a centurion of what was known as the Italian Cohort, ² a devout man who feared God with all his household, gave alms generously to the people, and prayed continually to God. (Acts 10:1-2)

22 And they said, “Cornelius, a centurion, an upright and God-fearing man, who is well spoken of by the whole Jewish nation, was directed by a holy angel to send for you to come to his house and to hear what you have to say.” (Luke 10:22)

Paul, too, had favorable encounters with centurions. One intervenes to prevent an unlawful whipping:

²⁵ But when they had stretched him out for the whips, Paul said to the centurion who was standing by, “Is it lawful for you to flog a man who is a Roman citizen and uncondemned?” ²⁶ When the centurion heard this, he went to the tribune and said to him, “What are you about to do? For this man is a Roman citizen.” (Acts 22:25-26)

And on Paul’s Iliadic seafaring adventure to Rome, he shared it with a centurion named Julius, about whom we read:

¹ And when it was decided that we should sail for Italy, they delivered Paul and some other prisoners to a centurion of the Augustan Cohort named Julius… ³ The next day we put in at Sidon. And Julius treated Paul kindly and gave him leave to go to his friends and be cared for. (Acts 27:1,3)

After Paul more or less takes charge of the doomed vessel and helps all hands to survive the shipwreck, the soldiers naturally express their gratitude by planning to kill Paul, fearing the punishment should he escape. But Julius saves him:

⁴² The soldiers' plan was to kill the prisoners, lest any should swim away and escape. ⁴³ But the centurion, wishing to save Paul, kept them from carrying out their plan. (Acts 27:42-43)

At first blush it would seem unlikely that the position of a professional Roman officer should be portrayed favorably in the New Testament. But on second thought, it makes perfect gospel sense.