I wrote this at the end of this last semester about how our faith relates to the profession. The suggestion there is modest, and there are questions beyond what that post covers that specifically pertains to Christians.
It has been suggested that we Christian philosophers should do philosophy as Christians, and so we might wonder about how we can do that, how separate from the academy we must be (i.e., how autonomous Christian philosophers must be as a community), how much revealed truth guides our research and writing, etc.
Beyond methodology, how we do philosophy, and how that relates to the academy, there are also other issues we as Christians should be concerned about. It is not a secret that in academia there is a degree of careerism and prestige. I take both careerism and an obsession with prestige to be contrary to what we are called to be as Christians, but how that manifests and how we can mitigate it are things we should talk about, as well as the impact on Christians coming into the profession.
That naturally enough leads into asking about the current drama in the profession over a particular scholar and ranking system. I don't know the answers to any of these issues, though, I just think they're important to highlight.
These past two paragraphs do not directly address your question because you're asking about what to study-- but philosophy is a profession, and so the profession and how to go about the business ought to be mentioned. As for content, there are a diversity of views here already: We might say that everything is open to study without qualification, or that everything is open to study once we've got a certain baseline, or that there are limits, or that the whole field is wrong-headed. I take both the first and last view to be wrong: Philosophy is clearly, as noted in the post linked, intertwined in a valuable way with the Christian faith. Further, it seems that if we genuinely are Christians and put God and faith in God above everything, we cannot without qualification do what we like-- there are certain baseline things if we are to do philosophy as Christians. So, I am sympathetic to /u/emperorbma here but also think there are limits-- maybe doctrinal limits, or maybe just practical ones. It would be unproductive for me, as a Christian, to work on certain things, and so I probably won't and it will be because I know them, in light of revealed truth, to be wrong.