How much stuff are you lugging? The 28X public bus will take you from the airport to within a walkable distance to the Amtrak station. I can't remember the fare, a few bucks. See http://portauthority.org/

If you exit on Liberty Ave before the bus turns on Seventh, (which it looks like you have to do back at Wood St), you'll be within a few blocks of the Amtrak station. Just walk straight up Liberty Ave. Since you're already downtown within a few blocks a transfer is probably more trouble than it's worth, but you can still ride within the downtown zone for free as far as I know. Many routes might take you another few blocks closer, but if you've got so much stuff you can't walk from where you exit the 28X, I think the public bus is probably not for you anyway.

Where are you going that you are transferring to Amtrak? Or just meeting someone there?