"Class" equates to social position: Upper Class, Middle Class, Lower Class, Professional Class, Labouring Class, Underclass. They are thoroughly confused and flexible. There is much argument at present over an actress who claims she is working class, but who grew up in a respectable suburb, had parents in respectable jobs, went to a private school and speaks in an educated way. She is redefining Working Class to suit her own purposes.
Someone who is "first class" implies someone of great probity, intelligence and achievement. It would not normally be used in the way you have suggested, but might be used to refer to a sportsman or someone who has achieved something.
I would avoid using the term unless you are intending to indicate the quality of something: It was a first class performance; They have done a first class job on the redecoration; That company can only achieve second class work as they will not employ good staff.
That is a description of the ticket rate for the plane - First class - most expensive; Business Class = expensive; Economy Class - the rest of the herd. It is not relevant to the nature of the passengers.
"Whose is this magazine?"
"I think that passenger from First Class dropped it as he went past."