I would only add to this excellent account that in the Septuaganit, εὐαγγέλια (evangelia) is used to translate the Hebrew word “besorah” בשורה usually translated as “good (or glad) tidings”. So the origin of “gospel” “good story” might go back to the OT.
It certainly does as Handel made popular. “O Thou that tellest/bringeth good tidings to Zion.” He sees it as a specific foretelling of the NT “Good Tidings” or “Good News”. It is interesting, to me at least, that besorah is a noun but it is the verb form that is used in Isaiah 40. “To tell good tidings”. The Septuagint uses εὐαγγελιζόμενος at that point and Luke 8:1 uses that verb form as well.
Of further interest to me, as I travel this trail, is that the etymology of euagglia is eú, “good, well” (hence euphemism, eulogy etc) and angellō, “to announce”. An “angel” is more properly a messenger--one who announces.
edit: So, καὶ ἀποκριθεὶς ὁ ἄγγελος εἶπεν αὐτῷ Ἐγώ εἰμι Γαβριὴλ ὁ παρεστηκὼς ἐνώπιον τοῦ θεοῦ καὶ ἀπεστάλην λαλῆσαι πρὸς σὲ καὶ εὐαγγελίσασθαί σοι ταῦτα
The angel said to him, “I am Gabriel. I stand in the presence of God, and I have been sent to speak to you and to tell you this good news.
Again a verb following Isaiah 40.