If I may, I encourage you to study the word "
covenant" in the Bible and how scripture asserts and uses the term because any discussion of Covenant Theology (CT) will be predicated, and best be measured by what scripture states. CT is largely associated with the Reformation and Reformed theology, but the truth is CT existed for centuries before the Reformation. Catholics, those of the Reformed persuasion, and their competitors (like Dispensationalists) are going to have much different answers and you won't know what to think about any of them if what scriptures states is unknown. CT has evolved over the centuries, and it is not monolithic. There are a core set of precepts that provide orthodoxy, or what might be called "
CT orthodoxy". Lastly, it's always best to consider the in-house case for any given position rather than taking only the appraisals of outsiders as true. I would, therefore, recommend you give one of the books listed
HERE a read or peruse some of the articles
HERE. Once you know what scripture says then any exegetical mistakes the CTers make will be recognized, and once CT is correctly understood from the pov of the CTers then any straw men asserted by critics can be recognized.
Personally, I also recommend "
Kingdom Through Covenant" by Stephen Wellum and "
Far as the Curse is Found," by Peter Gentry and Michael D. WIlliams. Gentry and Wellum write about what is known as "
Progressive Covenantalism," or the premise God's covenant is revealed incrementally, or progressively throughout scripture. Williams does an excellent job of surveying scripture to describe God's purpose in creation in a singular and cohesive manner. All three of these authors fall within the umbrella of Covenant Theology but hold views slightly different than the classic CT pov. After becoming familiar with CT and the RC and EO views you might want to explore the matter of continuity versus discontinuity because that subject is currently being richly debated among Christians do the effects of Dispensationalism and their view scripture is discontinuous (the rest of Christendom has long held the opposite view).