Here is a link to the Northeast Corridor rail schedule timetable brochure:
http://www.njtransit.com/pdf/rail/R0070.pdf
If you want to enter different stations and days of the week to pull up the schedule, look here:
New Jersey Transit
Parking is difficult at the Princeton Junction station. I don't park there often, just for the occasional trip up to NYC or to the airport. When I do park there, it's usually before 6:30 am and finding a spot is not yet an issue.
Depending on where you move in Princeton, there is a single car train ("the dinky") that runs between the Princeton Campus (University Pl near the Wawa) and the Princeton Junction station which could be a way for you to get there while you are on the wait list for a parking permit.
Parking at Hamilton is also a good option.