The word "gentiles" means "nations"- a term used by the Israelites to denote all foreign (non-Israelite) peoples. Thus, the term gentile would typically designate anyone who is not a descendant of Abraham through Isaac and Jacob.
Most today term someone a gentile who is not a Jew. But Judah, the father of the Jews, was only one of 12 brothers from whom the 12 tribes of Israel originated. Joseph, Benjamin, Simeon, Reuben, Dan, etc., were also sons of Jacob and their descendants would not be considered gentiles.
Later, when the locations and identities of the other family members of the northern 10 tribes (called the House of Israel) were lost when they were taken into captivity, the term "Jew"came to be used for all of Jacob's known family.
When the Bible refers to the Jews first, then the gentiles, it means that the descendents of Jacob, called Jews, were the ones who first heard the gospel message brought by Jesus. After that it went to the gentiles who lived outside Judea and Galilee.
Since circumcision was a sign of the covenant God made with the children of Abraham, it is a term often used to indicate a Jew as opposed to a gentile. Those "of the circumcision" would be a reference to Israelites. Although there are physical benefits to male circumcision, God does not require this today for Christian conversion. Romans 2:28-29 says that what God really wants is spiritual circumcision of the heart - a repentant, godly attitude.