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Jesus' ministry was to the Jew to fulfill the covenant promises that were spoken about through the old testament.

Luk 1:72 To perform the mercy [promised] to our fathers, and to remember his holy covenant;
Luk 1:73 The oath which he sware to our father Abraham,

Romans 15:8, "Now I say that Jesus Christ was a minister of the circumcision for the truth of God,to confirm the promises made unto the fathers: Abraham, Isaac, and Jacob

Jesus' himself told them not to go to gentiles.

Mat 10:5 These twelve Jesus sent forth, and commanded them, saying, Go not into the way of the Gentiles, and into [any] city of the Samaritans enter ye not:

Mat 10:6 But go rather to the lost sheep of the house of Israel.

Mat 10:7 And as ye go, preach, saying, The kingdom of heaven is at hand.

Matthew 15:24, "But he answered and said, `I am not sent but unto the lost sheep of the house of Israel.'"

He was rejected by his covenant people. He died on the cross and still he tried to get the Jews to recognize who he was but they would not. After Steven was stoned, He saved Saul and sent him as Paul to preach to us gentiles. Paul is sent as a vessel from Jesus to the gentiles.

Act 9:15 But the Lord said unto him, Go thy way: for he is a chosen vessel unto me, to bear my name before the Gentiles, and kings, and the children of Israel:

Rom 11:13 For I speak to you Gentiles, inasmuch as I am the apostle of the Gentiles, I magnify mine office:

Rom 11:7 What then? Israel hath not obtained that which he seeketh for; but the election hath obtained it, and the rest were blinded

Rom 11:8 (According as it is written, God hath given them the spirit of slumber, eyes that they should not see, and ears that they should not hear;) unto this day.

Rom 11:9 And David saith, Let their table be made a snare, and a trap, and a stumblingblock, and a recompence unto them:

Rom 11:10 Let their eyes be darkened, that they may not see, and bow down their back alway.

Rom 11:11 I say then, Have they stumbled that they should fall? God forbid: but [rather] through their fall salvation [is come] unto the Gentiles, for to provoke them to jealousy.

Rom 11:25 For I would not, brethren, that ye should be ignorant of this mystery, lest ye should be wise in your own conceits; that blindness in part is happened to Israel, until the fulness of the Gentiles be come in.

Paul is sent as a vessel from Jesus to the gentiles.

Actually, the first conversion was as the result of the ministry of St. Peter.

In the verse you cited from Acts 9, Saul had just gotten healed by Annanias. Paul did not begin his ministry to the Gentiles until Acts 13 (Acts 13:2 While they were worshiping the Lord and fasting, the Holy Spirit said, "Set apart for me Barnabas and Saul for the work to which I have called them.").

In fact, Peter received a vision from God in Acts 10:10-16. He then had his encounter with Cornelius (Acts 10:17-48). He then shared what had happened in Joppa with the Church in Jerusalem...When they heard this they were silenced. And they glorified God, saying, "Then to the Gentiles also God has granted repentance unto life." (Acts 11:18). The point is that had this not happened, it is very unlikely that Saul (who became known as Paul in Acts 13), would have ever ministered to any Gentiles.