Should you translate ἡ βασιλεία τοῦ θεοῦ as “the kingdom of God” or “the rule of God?” I favor rendering it as “the kingdom of God,” but technically, I think you can do it either way. If you have an interest in this topic, or know Greek, I encourage you to read what Hank has to say and contribute to the convo over there.
Jews or Judeans? There has been some debate as to whether or not the use of the term “Jews” is an appropriate translation of Ἰουδαῖοι. There are a slew of posts on this topic over at ΕΥΑΓΓΕΛΙΟΝ on this topic. See Judean and Syrian, and Being a ‘Jew’ or a ‘Judean’. Elsewhere you can find John H. Elliott’s article on Jesus the “Israelite” and Was there such a thing as ancient “Judaism”?: Steve Mason’s recent article on “Judeans” (Ioudaioi) in antiquity. Me? It depends on the context and who is writing. I think that most of the time "Judeans" should be used in the gospels, but in other sources, such as Paul’s letters, "Jews" should prob be used.