Hebrew, Aramaic, and Greek were some of the languages used in the area and its surrounding region. Neither the Hebrew Bible nor the Christian New Testament were written predominantly in Aramaic, in fact the vast majority of the Text is in Hebrew or Greek.
It is worth pointing out that few scholars believe any portion of the NT was written in Aramaic, although there is much work on how Semitisms influenced the tradition behind the texts. Also, as you are an archaeologist, I have a question related to (or subfields of) archaeology in Judaea and Galilee in and around the first question. I am pretty sure we have onomastic and I believe epigraphic evidence for Latin in and around Galilee in the first century (see e.g., "The Galilee Jesus Knew"). Do you happen to know what evidence exists for the attestation that other languages (Phoenician, its offshoot Punic, offshoots of other languages spoken in the Near East/Mediterranean such as Edomite, Moabite, etc.) were used at all in and around the 1st century and in and around Jerusalem & Galilee?
Thanks.