Generally, the Fathers spoke highly of the pope of Rome because he was the head of the Church and because he was orthodox in faith and practice. The problem is in trying to take these compliments and form a theology around them. If you look at what St. Gregory the Theologian said about St. Basil
(or St. Athanasius
), for example, you would think that St. Gregory spoke with what appeared to be almost god-like reverence. In fact, Sts. Basil and Gregory had something of a rocky, love-hate friendship, especially later in life. Obviously there was some discontinuity between rhetoric, reality, and theology, and while I'm certainly not going to accuse St. Gregory of lying , I'm also not going to take literally St. Gregory's words that paint St. Basil as greater than all the apostles, prophets, etc. The point was, Basil was great and Gregory wanted to say so. Reading more into it than that will lead to ruin. We find something similar with many of the quotes from the Church Fathers about Peter. Various Fathers will say that Peter is the rock, that Peter holds the keys, that Peter was the leader of the apostles.
This is all very true, but it is not the end of the story. There is much more, both alternative views of these things (the rock, the keys, etc.), and various evidences that show that all of this ta-do about Peter meant absolutely nothing apart from doctrinal orthodoxy and practice. Catholics often bring up some of St. Cyprian's words about the place of Rome, for example, and certainly St. Cyprian said many high things about the see of Rome. Yet, these words did not prevent St. Cyprian from later getting into a doctrinal dispute with the Pope of Rome: a doctrinal dispute which showed that he neither felt the Pope to be infallible nor having jurisdiction over him.
The history of Constantinople is like an ongoing history of battling claims of primacy within the Church. Just looking at an overview of the 4th century can be interesting. Catholics sometimes quote St. John Chrysostom (Archbp. of Constantinople at one point) to defend papal supremacy. Interestingly, they normally do not mention that Rome was not in communion with St. John's predecessors, St. Nektarios and St. Gregory the Theologian. Rome wasn't in communion with them, but most of the rest of the Church was, and it didn't matter a whit that Rome hadn't given the ok for St. Gregory or St. Nektarios to be patriarchs. In fact, ignoring it's own history (e.g., St. Ambrose of Milan), Rome tried to argue against the elevation of St. Netkarios on canonical grounds, and never did recognize him. Rome's "supremacy" did not extend into reality at that point (as it would later extend into reality in the west), and the easterners just went about their ecclesiastical business. The same thing can be said about canons not accepted by the Roman Church, but always accepted by eastern canonical law. Rome was the leader, and Rome was lauded as being important, but when it came down to the task of actually administering the Church, each bishop or local council of bishops did what they thought best.
Lists of what the Church Fathers said are fine. The important thing is just to have a context in which to understand them. If you want to know about papal supremacy, I would suggest reading lots of books on the history of the early Church--from all different perspectives. Anglican, Lutheran, Orthodox, Catholic, I've seen historians in all sorts of churches who bring something good to the table that others haven't. And the longest or most detailed histories are not necessarily the best ones either; sometimes a short one which happens to mention some unique situations rarely mentioned elsewhere can open up whole new lines of exploration which you otherwise would have missed. If you have a specific stumbling block (quote) in mind, I'm sure many people here would be glad to offer an alternative interpretation or two. But generally speaking, the best thing to do is just to dig into it and let history itself say what it wants to say.