To which I'd add: Take a walk through Reading Terminal Market. Interesting mix of shops and food opportunities (including excellent Amish apple dumplings--ask for milk to pour over it).I don’t understand the “Center City station” reference either. I’d just ignore it.
The two “freebies” connecting from Amtrak at 30th Street are Suburban Station and Jefferson Station (which used to be called Market East and is nowhere near Jefferson hospital—they just threw money at SEPTA to get their name used). Very unlikely that anyone will look at your ticket on the train itself—they change crews at Suburban so are busy with that.
Suburban brings you out near City Hall and Macy’s.
Jefferson Station is at the convention center and across the street from Reading Terminal Market.
I prefer Jefferson because I always get lost in Suburban and always, always end up at the exit with a steep set of stairs to the street and can’t figure out where I am at the top. Jefferson is a bit easier for those like me with little sense of direction.
I hope you have a wonderful time in Philly! Make sure to take in the lovely main hall at 30th Street.
Also, if you have time, go to Macy’s to look at the Eagle, and look for Billy Penn standing at the top of City Hall looking out over the city (and maybe saying “I need a break—which way to Pittsburgh?”).