I spent at least a month in each on my first trip, and Rick's tours spend two weeks in each, to hit the highlights. Therefore, I recommend choosing only one country for this amount of time.
If you do both, then plan to fly into Athens and out of Istanbul (multi-city or open-jaws flight), so that you don't have to double back. Also plan to fly between those two capitals. Or there are also a few flights between Greece and Izmir, near Ephesus; see www.skyscanner.com.
To cross Greece by ferry requires a long overnight ferry ride or a few connections between different island chains. Once you are on the neighbor islands with ferries that cross to Turkey (such as Lesvos-Mytilini, Samos-Kusadasi, Kos-Bodrum, or Rhodes-Marmaris), you usually must buy the international ticket at least the night before taking that ferry, for passport registration.