There is no size limit in their stated policy so I would think any size would be okay.
The security screening at the ship is much the same as at the airport; except you don't have to take off your shoes. You do have to empty your pockets and pass through a metal detector, and your carry-on bags are x-rayed and sometimes visually inspected.
I can't think of anything that should be avoided; quite the contrary, I would say, "go for it!."