When you have two or more options, and there is one you prefer the most, you can say I`d rather, which means "prefiero". In Spanish we use the term "mejor" not only as a comparative but to express some degree of preference. In this case you should say "I´d rather eat a banana." That´s to say you prefer the banana and not the apple you mentioned in your example.
Other example is:
- Do you want to go to the movies?
- No, I´d rather stay home.
-¿Quieres ir a cine?
- No, mejor me quedo en casa.