For I handed on to you as of first importance what I also received: that Christ died for our sins in accordance with the Scriptures; that he was buried; that he was raised on the third day in accordance with the Scriptures; that he appeared to Cephas, then to the Twelve. After that, Christ appeared to more than five hundred brothers at once, most of whom are still living, though some have fallen asleep. After that he appeared to James, then to all the apostles. Last of all, as to one born abnormally, he appeared to me (verses 3-8)Paul calls himself "the least of the apostles" and writes that he is "not fit to be called an apostle, because"- here he is referring back to events recorded in Acts chapters 7-9, including the stoning of Stephen- "I persecuted the church of God (verse 9)." While Paul may not have felt himself fit to be called an apostle, he is an apostle because the Risen Lord saw fit to appear to him on the road to Damascus, where he was headed after Stephen's stoning, armed with a letter from the Sanhedrin in Jerusalem, to conduct further persecutions of those he viewed as apostate Jews.
Worthiness is never the issue. What God calls you to do, He will equip and strengthen you to do. As the apostle wrote in his First Letter to the Thessalonians (the letter that vies with First Corinthians as the first book of the New Testament to have been written), "The one who calls you is faithful, and he will also accomplish it" (1 Thess. 5:24).
While we are not all called to be apostles- there were ever only 12- or successors of the apostles (i.e., bishops), or priests, or even deacons, we are all called and, by virtue of our call, sent (apostle means one who is sent) to bear witness to what St. Paul captures in this earliest Christian creed. This is why Roman Catholic "ministries" are more appropriately called apostolates.
Of course, you cannot be a witness to an event you have not experienced. Like St. Paul, you can only witness the event of Christ's glorious resurrection by way of an encounter, an experience, which is not just something happens to you, but something that moves you. I employ "move" here not in a sentimental sense, but literally, it is something that causes you do something, provokes a response from you.
Pope Benedict XVI articulated this well towards the very beginning of his first encylical letter, Deus caritas est, in what is without doubt the most quoted sentence from that popular letter: "Being Christian is not the result of an ethical choice or a lofty idea, but the encounter with an event, a person, which gives life a new horizon and a decisive direction" (par. 1).