I believe that officially First Class is only found on the Acela. However most people consider Sleepers as First Class, as that's what they essentially are.
System-wide Amtrak has 5 'levels' of Service:
Acela First Class
Sleeper Car Service
Business Class
Coach Class
peter
Um, I think that is four classes, not five.
Here is my understanding of Amtrak classes:
LD trains: Coach and Sleeper Classes
SD trains: Coach and Business Classes, latter is not always available
Acela: Business and First Classes
Some trains do not fit this list.