You have to change trains at Jamaica unless you get the 5AM train into Penn. The parking is convenient at the stations, but the service on this line is a nightmare. Always packed and always transferring. Many people in the area prefer parking at a friend's house in Manhasset or Great Neck and taking that LIRR line instead.
As for the crowds, delays, etc. much will depend on the start/end time of your commute, weather conditions, etc., why not take the time and consider a test run, generally it will take about an hour into Penn Station... http://lirr42.mta.info/