Modified would be my first choice. However before you go out to get the clays test your chokes on a pattern target at range to be sure what you getting. Make sure you are using the same ammo..
BINGO........................I use a full and an improved modified for trap. The IM for up to the 20. After that full. For skeet I use a skeet choke or cylinder.
The senior national sporting clay champion manages the course I shoot at a lot. I have borrowed his guns and shot with him many times. I have never seen him shoot a full choke at any clay. You mean he won a national title by doing it wrong? I guess some folks have the luck of the Irish.Every range I go to the birds fly the same so the same choke and shot that works for you is all you need.
gvw3 has it right.