Paul's profession was tentmaking. According to Acts 18:3, when Paul arrived in Corinth during his second missionary journey, he stayed and worked with Aquila and Priscilla "because he was a tentmaker as they were." In the Greco-Roman world, tentmaking involved working with leather and cloth to produce tents, awnings, and similar goods.
Paul used his trade to support himself financially during his missionary travels so that he would not be a burden to the churches he was planting (1 Thessalonians 2:9, 2 Thessalonians 3:8). He viewed this self-sufficiency as an important aspect of his ministry and a model for other believers. In 1 Corinthians 9:12-15, Paul explained that although he had the right to receive financial support from the churches, he chose not to exercise that right.
The other professions are associated with different biblical figures. Carpentry is traditionally associated with Joseph, Jesus' earthly father (Matthew 13:55). Fishing was the profession of several of Jesus' disciples, including Peter, Andrew, James, and John (Matthew 4:18-22). Shepherding is associated with figures like Abel, Abraham, Moses, and David, but not with Paul.