Real Dictionary

first class in American English
noun: the best, finest, or highest class, grade, or rank

first class in British English
of the best or highest class or grade
noun: the class or grade of the best or highest value, quality, etc

first-class
adjective: If you describe something or someone as first-class, you mean that they are extremely good and of the highest quality.

first-class in American English
adjective: of the highest or best class or quality
adverb: by first-class conveyance

first-class in British English
of the highest class, rank, excellence, etc.; of the best quality
adjective: (of rail or air travel) offering a higher level of comfort