If English is your primary language, probably the easiest way to go about building your Patristic library is to work your way through St. Vladimir's Popular Patristic series: http://www.svspress.com/index.php?cPath=43_8_16
You'll get good introductions, notes and readable translations of many of the seminal authors, including selections that deal with dogmatics (especially Christology), iconography, liturgics, sacraments, asceticism, social outreach, prayer and mysticism.
If you don't mind sending your money to the Big Daddy of Protestant/Christian book sellers, then buy them here at a discount: http://www.christianbook.com/Christian/Books/cms_content?page=1192577&sp=85684
Personally, I would also snag a copy of the Apostolic Fathers (those from the early second century) and read those first. I recommend The Apostolic Fathers: Greek Texts and English Translations
by Michael W. Holmes, since it has the most up-to-date manuscripts and translation, but there are many other volumes available, including some that are in the public domain, so you could read them online for free (for example, http://www.ccel.org/fathers.html
, where you can also read old translations of many important Patristic works that aren't in the SVS series).
After reading the Apostolic Fathers, I'd work through some of the most important entries in the SVS series in this order (kind of influenced by chronology, but mixing it up occasionally for the sake of thematic variety):
On the Apostolic Preaching: St Irenaeus of Lyons
On the Apostolic Tradition: St. Hippolytus
On the Christian Sacraments: St Cyril of Jerusalem
On the Incarnation: St. Athanasius the Great
On the Holy Spirit: St Basil the Great
On Ascetical Life: St Isaac of Nineveh
On God and Christ: The Five Theological Orations: St Gregory the Theologian
On the Unity of Christ: St Cyril of Alexandria
On Wealth and Poverty: St John Chrysostom
On The Divine Liturgy: St Germanus of Constantinople
Three Treatises on the Divine Images: St. John of Damascus
On Marriage and Family Life: St John Chrysostom
On the Cosmic Mystery of Jesus Christ: St. Maximos the Confessor
On the Mystical Life, Vols. I, II & III: St. Symeon the New Theologian
Mix it up even more if you want, and, of course, move on to the various other entries in the series thereafter. There are probably about 12 others in addition to the ones listed above.