For me the Turkish grind is king but I don't like the miserly portion of a traditional Turkish. When I have access to good beans I'll get a bag of it in fine Turkish grind and keep it in the freezer. To cook the coffee I add a two or three tablespoons to a saucepan and bring it to the boil, then pour.
Once in the Middle East I came across a cafe that does it in a similar way, that is a much larger than standard Turkish. They managed to filter it in some manner too and it was delicious. Turkish coffee will not go through normal filter paper and so I don't know how they managed it. When I do my own I just let the sediment sink to the bottom of the cup like a normal Turkish.
If Turkish grind, or great beans aren't available I'll just get a regular medium grind from a supermarket or coffee shop and put it through a peculator.