Stick with the driving. On the 73 you will have a line in less than 6 months at the current rate. Most of the time on reserve you will be long call and a 2.5 hour drive is a non issue. As far as short call you have several things going for you. NYC pilots have a special consideration for traffic and are given some leeway for getting to work in a short amount of time. Don't make a habit of being late though, especially on probation. If your bag is packed and you are basically ready to walk out the door on SC I think you will be fine sitting at home. 90% of the trips I get assigned off short call I get more than 2.5 hours notice. I would say 3-4 hours notice is typical. Constantly keep an eye on your schedule on CCS when on SC and you will almost always know you are going to work before 2.5 hours out.
Good luck and welcome!