First class seats on the Acela Express are the only seats which can be reserved prior to check-in, anywhere in the Amtrak system.* In fact, they are automatically assigned—you cannot see the seat map, and do not know what you have been assigned until you have purchased a ticket, though you can change it afterwards online or with an agent for no charge.
Can I choose a specific seat?
Not while you're making a reservation. Your seat will be automaticaly [sic] assigned to you when you complete your reservation. You may change your seat assignment and choose a different seat at any time after the reservation is complete. Just view your reservation in the Amtrak app or on Amtrak.com. There is no fee to change your seat.
(from Amtrak's First Class Seat page).
Note that the Acela Express is a unique service in the Amtrak system, and does not have a coach section. The "regular" seats are marketed as business class, and the premium seats as first class. This doesn't make a practical difference in terms of seating selection, however, as neither business nor coach seats cannot be reserved in advance on any train in the system.
On long-distance trains, the conductor may assign you a seat, or may allow you to take any open seat. This is largely dependent on how crowded the train is and, for example, if they are anticipating any groups boarding down the line to keep together. For the same reason, even if you are directed to choose your own seat, you should notify the conductor if you want to change later on. On corridor services like the Northeast Regional or Keystone, seating is generally a first-come, first-served scrum, though the conductor will help you find a seat if you ask.
* Rooms and roomettes on trains with sleeper cars are requested and assigned in advance, but these aren't "seats" of course.
