The immediate text gives no hint, but later on in the same chapter, Luke relates important criteria of apostles in his version of Jesus' key sermon (The Sermon on the Plain). The sermon is delivered to "his disciples" but of course, the 12 apostles are included in this category.
27 “But to you who hear I say, love your enemies, do good to those who
hate you, 28 bless those who curse you, pray for those who mistreat
you. 29 To the person who strikes you on one cheek, offer the other
one as well, and from the person who takes your cloak, do not withhold
even your tunic. 30 Give to everyone who asks of you, and from the one
who takes what is yours do not demand it back. 31 Do to others as you
would have them do to you... 36 Be
merciful, just as [also] your Father is merciful.
In Chapter 10, Jesus praises God for giving him apostles/disciples who are childlike:
He rejoiced the holy Spirit and said, “I give you praise, Father, Lord
of heaven and earth, for although you have hidden these things from
the wise and the learned you have revealed them to the childlike. Yes,
Father, such has been your gracious will." (Luke 10:21)
This may be a clue as to central criterion the Father sought in Jesus' closest followers. (It comes shortly after the sending of the 72.) Earlier in the same chapter, Jesus gives the following instruction to these missionaries:
Carry no money bag, no sack, no sandals; and greet no one along the
way. 5 Into whatever house you enter, first say, ‘Peace to this
household.’ ...7 Stay in the same
house and eat and drink what is offered to you, for the laborer
deserves his payment. Do not move about from one house to another. 8
Whatever town you enter and they welcome you, eat what is set before
you, 9 cure the sick in it and say to them, ‘The kingdom of God is at
hand for you.’
We can infer from this that Jesus sought representatives who relied on God to provide for them and made spreading the Gospel their top priority. He hoped for apostles who manifested the qualities of Luke's version of the Beatitudes.
In Chapter 9, Luke relates another key quality of discipleship expected by Jesus:
“If anyone wishes to come after me, he must deny himself and take up
his cross daily and follow me. 24 For whoever wishes to save his
life will lose it, but whoever loses his life for my sake will save
it.
The OP asks about apostles in the main question. Later, it refers to assistant ministers and other church officers. However, the qualities Jesus looked for in his apostles may not be analogous to the qualities needed in a settled church. The apostles had to be willing to face serious persecution and even literally give their lives for the Gospel. They had to go out with no money and rely solely on God and the generosity of the people to sustain them. They needed to feed the poor and heal the sick directly - not by raising money from a congregation or giving to institutional charities. So God's criteria for apostleship in Jesus day required a very high level of commitment, faith and humility. His criteria for church officers, while certainly requiring these qualities, also involve professional abilities such as being a competent public speaker, counselor, administrator, fundraiser and organizer.
In sum, Luke emphasizes the criteria of being childlike and making a life-and-death commitment to the Gospel at the expense of all else. But elsewhere he provides many other clues as TO the qualities the Father sought in Jesus' apostles.