The Apostolic Fathers such as 1-2 Clement, Ignatius of Antioch, Polycarp (and the martyrdom of Polycarp), Didache, Justin Martyr, Letter of Diognetus, Papias, Shepherd of Hermas, Barnabas, and even Irenaeus who is considered sub-apostolic because he was within the next generation. Also there are some good apocrypha New Testament writings. You can find them all right here
litteralchristianlibrary.wetpaint.com/page/Early+Church+Fathers+Collection
I recommend not just limiting your study on the Apostolic Fathers but to study all the Church Fathers such as Clement of Alexandria, St. Augustine, St. John Chrysostom, St. Jerome, all the St. Gregorys (the Great, Nazianzen, of Nyssa), St. John of Damascus, St. John Cassian, St. Ephrem the Syrian, etc, etc.
Plus the Doctors of the Church like St. Thomas Aquinas