I described here some of the assumptions I made in the original post. From them it follows that the only universal context for the whole humanity is the reality itself, because any other context is subjective. I also touched the "my truth != your truth" problem. Hope my explanation won't create even more confusion :-)
About asking the most difficult question first, I think you would get stuck pretty early. It seems to me that a good approach might be to always have a whole spectrum of unanswered questions, with increasing difficulty. Some of which could be addressed today, some within a week, within a month, year, lifetime (the exponential increase is intentional), as long as there are some left unanswered.
Nobody knows what the reality is actually, you can ask any quantum physician :-) I have been reading, though, about what this common ground could be and it seems that it could be consciousness itself. Some people are talking about changing the current paradigm to put consciousness above matter. Doesn't even seem to be anything new really. Peter Russell gate a rather interesting talk about this.
Talking about the sorting of questions, for me it seems that there are multiple completely different types of questions so to say. For example talking about consciousness, how do you want to touch that field without simply using your consciousness and nothing else? These questions are completely different from those answerable using mere words to me. And researching consciousness is a funny thing. You never know what and when is going to happen. Try to come up with a sorting :-)