It is important, I think, if you're going to place a premium on historical continuity/consistency, to look at the churches that the Apostles themselves established, e.g., the Antiochian Church, the Alexandrian/Egyptian (Coptic) Church, the churches of Constantinople, Jerusalem, etc (mainly Byzantine/EO in our times).
Careful study will show that the Rome-affiliated sections of these churches (e.g., Byzantine Catholics, Coptic Catholics, etc.) came along much, much later, starting in the 1500s or so (or 1100s, if you take the Maronites as a section of the Antiochian Syriac Church, though their particular form of Christianity cannot be dated back earlier than the 5th century, as that was when Maron died, and the church named after him was founded after his death). So they're, in that historical sense, not candidates as apostolic churches. Rome herself would be, of course, were it not for the fact that the Orthodox view of apostolic succession is faith-based, rather than simply "man-based" (for a lack of a better way to put it; I refer here to the RC/Western idea of "Episcopi Vagantes"), meaning that if the faith itself is not preserved from error, it does not matter who did the ordaining -- the line itself is broken because the faith is not the same. This is also what keeps the Church of the East/Nestorians out of the discussion.
So with all of these things in mind, you should now ask yourself who you are left with. It is only the Orthodox who fit the bill, as the others either came about much, much later (Protestants and Eastern Catholics), or are old enough to trace their church's founding directly to the apostles, but have changed the apostolic faith in some way and hence become 'apostolic' in name only, not in content (Rome and the Nestorians).
