The word commonly translated as "carpenter" is the Greek word tektōn (τέκτoν). A more strict translation might be "craftsman" or even simply "worker." There's an association with working with wood, but that is far from absolute. Likewise there's an association with being skilled, but that also not absolute. It definitely was used more in the context of buildings not furniture. So your mind should go to a roofing type of carpentry not a cabinet making form of carpentry.

The word could be used for a master woodworker making beautiful and functional buildings. It could also be used for a day laborer piling rocks to make a rough goat pen.

We don't know precisely where on the scale Jospeh and Jesus fell. We do know the one place that they were called tektōn, it was in derogatory sense.

Jesus left there and went to his hometown, accompanied by his disciples. When the Sabbath came, he began to teach in the synagogue, and many who heard him were amazed. "Where did this man get these things?” they asked. “What’s this wisdom that has been given him? What are these remarkable miracles he is performing? Isn’t this the carpenter? Isn’t this Mary’s son and the brother of James, Joseph,Judas and Simon? Aren’t his sisters here with us?” And they took offense at him. Jesus said to them, “A prophet is not without honor except in his own town, among his relatives and in his own home.”

Given the context it's pretty clear that tektōn was not considered a prestigious position. It's likely that Jesus and Joseph would have been "semi-skilled laborers" and would have fallen among the poorer people in Galilee.

How much wood was available around Nazareth at the time?