Philadelphia International Airport (phl) is well-connected to the city via the Airport Line, one of the Regional Rail lines operated by SEPTA, the local transit authority. This is by far the most reliable way to get from the airport to the Center City area. See SEPTA's Service to Philadelphia International Airport page for more information.
The Airport Line departs every half hour, 7 days a week, and the ride to University City near the Penn campus takes about 20 minutes. On-time performance for the line, at this writing, is 83%. The airport stops are located across from baggage claim
The airport stops are in Zone 4, and University City is in Zone CCP (Center City Philadelphia), and weekday Zone 4 fares are charged at all times.
Depending on your final destination at Penn, another alternative is to get off one stop early at 30th Street Station and either walk or take the LUCY Shuttle bus ($2.25).
SEPTA is a commuter system, and the train cars do not have luggage racks or closets; however, the airport is at the end of the line, so the train should not be overcrowded, and you may be able to find a seat at the bulkhead where there is more space.
This is a busy line and patrolled by the SEPTA Transit Police. Crime is more associated with Philly's subway lines than with the commuter rail, though it is possible as it would be in any transit system in any major U.S. city. (Don't read too much into the heat map that floated around the net a few years ago, as the developer himself warns, and which anyway excludes the airport stops).