I too would choose an upper level seat, if climbing stairs is no problem. I don't even know why they offer that option. (You can choose any available seat on the train.)
Unlike an airline flight, there is no real check-in or seat assignments. Once you board, you can have your choice of any available seat. (Personaly, I choose the window seat at the back half of the window. Each is 2 rows wide. This way, you can see out farther without obstruction.)
The only time you need to check-in in advance is if you are checking bags. (More than 30 minutes in advance.) Also some stations have a check-in in advance of boarding. (I'm not sure if SEA is one of those.)