Yeah, if you're going just one way from NYC to Philly, go with the Chinatown bus (10 bucks one way, 20 round trip). In NYC, the ticket both is at E. 88th and Broadway. Make sure you get on a 2000Coach bus. Trust me, you'll get swarmed with people trying to get you to go on their bus if you look lost, so just make sure! That will take you to 11th and Filbert (right in Center City), and from there you can take SEPTA (the subway system) on 12th and Market to Penn's campus. If you're going to stay over night, I would definately go outside of Philly. Anywhere about a half hour away should give you a good price. Also, if you don't want to take the Chinatown bus, go with Greyhound's 24 dollar roundtrip deal. It'll take you from port authority to 11th and Filbert.
For a cheap rental car, you could go with PhillyCarShare. I haven't tried it yet myself, but it looks like a good deal.
http://www.phillycarshare.org/html/students.htm
Good luck!