You should check the tranny dip stick and make sure that a: there is fluid in the trans, and b: that the fluid doesn't look terrible. It should be reddish and somewhat translucent. I would also recommend getting at least a qt of trans fluid to compensate for any fluid that spills out when we drop the trans.
Is this parking lot anyplace that you could leave the car for awhile if the problem is in the trans itself?
You are also going to need to get a 32 mm axle nut socket, they are usually a free rental at most auto parts stores unless someone else has one who is coming.