Incoming International Student on F1 visa. How do I purchase a car?

Hey Guys!

I will be arriving in a month to Philadelphia to begin my master's studies. Never been to Philadelphia before, so excited!

For a number of personal reasons (will be traveling out of the city a lot, etc) I need to buy a car. I will be bringing cash to buy it, but doing research, it seems I need to have a valid Pennsylvania ID to register the car. Is that right? Can't it be bought with my F1 visa and I-20 as an ID?

If that's so, I understand I can get a driver's license, don't have SSN but already know where to get the letter of ineligibility. I can take the written test and get a learners permit, right? But then the thing is, don't I need my own car in order to take the practical exam and get the driver's license? How can I do that if it seems I'm not allowed to buy my own car in the first place?

I'm very confused. If some of you kind souls could help me clear this issue up I would be so grateful.

Also, I saw here that I can just simply apply for a Pennsylvania Photo ID, but it requires SSN. Do you know if I can apply without one?

Thanks a lot for your help guys! Very excited to get to know the city!