You will be just fine. Celebrity tend to be a bit more of a dress-up line, but we've noted more trend toward casualness. I sometimes wear a tux for formal, but my last cruise on Century, I just did a dark suite.
Burger and fries are available everyday at the grill on the pool deck, this is for lunch time eating. In the dining room, you really need to try some of the different dishes. The beauty is, if you don't like it, they are MORE THAN GLAD to bring you something else. So, it's not like a land restaurant that if you try something and hate it, your still stuck with it or paying for something else. SERIOUSLY, don't be hesitant to tell them you want something else if you don't like the dish served. They get more concerned if you DON'T tell them. On the other hand, for people who don't want to experiment, although it's not always listed, they always have a steak available (sirloin usually) and Salmon. They always have a caesar salad available.
You'll have a great time on Century... don't worry so much, and go have a great time! We always do.
paul