I've read most of the letters by Ignatius of Antioch (essential as he was a leader in the early church of Antioch who quite likely knew John and is reported to have been ordained by Peter and/or John---also he was eaten by lions) as well as sections of Irenaeus's Against Heretics, selections from Clement of Alexandria (Stromota), Cyril of Jerusalem, Maximus the Confessor (not found in Western collections but readily available in the Philokalia),
Polycarp, I Clement (essential for seeing early mention of general idea of Apostolic succession--also likely a friend of Paul's mentioned in Philippians 4), selections from Eusebius' history, Hippolytus of Rome, the historian Socrates (NOT the philosopher who was before the time of Christ), bits from the Cappadocians (Basil, Gregory Nazianzus, and John Chrysostom), Augustine (of course), and a bit from some others here and there. Definitely useful in exploring what the early Church throught about certain issues and such. You can find most of the writings for these online at newadvent.org--just go there and look to the right for the tab for "Fathers."
A small word of caution: it may be useful to distinguish those who were canonized as saints from those who were not. For example, Origen had ideas which were later deemed heretical, as did Tertullian though I believe both died in good standing with the Church after having some difficulties. Those who are saints though not inerrant,
are safer overall though the others are still very important in understanding early Church discussions etc.
Glad someone is interested in these, graybeardheadbanger