The "exposition of faith" (expositio fidei) or "statement of faith" is quite common. The early Church fathers often summarized an exposition of faith, and today, many Christian websites, especially those of churches, summarize a statement of faith for all to see.
What do most statements of Christian faith include? I know this is relatively subjective, but there does tend to be some consensus among the many I have seen.
Any listing of specific doctrinal statements would be, as you noted, subjective, and therefore not constructive per site guidelines. The best answer that I can think of that would fall within site guidelines would be to give a generic answer that's applicable to all. The approach I'm going to take is the same approach that I'd take if someone were to ask me "what should be on my resume?" while looking for a job.
The things that should be included in a statement of faith should be those doctrines that the Church/denomination in question places importance on. This helps people that are trying to choose a Church to know what the Church teaches, and helps them to avoid wasting their time on one that teaches false doctrine. In general, that should include:
Beyond that, it may also include any of the following if the Church/denomination in question deems them as central teachings
In short, the included elements are entirely dependent on the teachings of the Church. The items in the top list are those that are likely going to be important for an outsider to do an "at-a-glance" evaluation on what the Church teaches. They're the types of things you'd want to know if you're in a new city looking for a Church to attend, or if you're shopping for a new Church. If those all fall in line with sound doctrine, then you can move on to the items on the second list.
These items are still important, but less agreed upon. The first list are items that most Christians would agree on, and if something "smells wrong" in that list, it should be easy enough to write off that Church as being wrong. The secondary items might help someone who is sure of their beliefs to find a Church that more closely aligns with his or her beliefs.
As stated in the question, this is a subjective topic, but I think a few things can be said.
The purpose of statements of faith (SOF) are usually two-fold. Very often they are an attempt to simultaneously explain the following:
Thus a SOF for an individual, ministry or church usually is not intended to define what is orthodox and what is heresy, unlike the creeds that were put down in e.g. Niceae, Constantinople or Chalcedon, but to affirm that one considers oneself as aligned to orthodoxy.
A SOF may be used to answer critics, clarify teaching and be a general guide of what to expect, sort of like content declarations for food. Thus, when a list of beliefs are being presented it is often hard to tell exactly what weight is being put on each item. There is usually no difference being made between:
Perhaps one should not differentiate between every item on that list, very much depending on what type of organization it is, but I still think reasoning along such lines would clarify a lot. Or to put it differently, what is being thought of as necessary and what is being thought of as beneficial?
There is also the question about how one reads a SOF. Is it intended to be understood as propositional truths or as general alignment with a tradition? E.g. when stating that one follows the Nicene creed, does that mean a general affirmation of its main thrust, or that one has accepted the neo-platonic metaphysics that guided how the church fathers wrote its details?
On the other hand, providing to much detail may attract pointless criticism and heresy hunters and would make the SOF harder to maintain, since it would need constant upgrades as new knowledge is gained.
