No jeans and no trainers to dinner on the one I went to. But you could dress as smartly as you wanted. On the Disney cruise and some of the American based ones, wear whatever you like, just as long as you wear something.
Drinks packages are a rip off. Unless actively you want to drink to paralysis every night. In which case you would look pretty out of place on the ship, where most people are in their cabins by 11.