If you haven't done it, you could clean the MAF sensor and the throttle body. Both are quick and easy jobs and may help with the rough start. Also, if the car has stood for a long while, old fuel will be an issue. Give it a fresh take of decent fuel and drive it hard and consider adding a can of BG44K. I've found it to be decent stuff; others may have alternative (and cheaper) recommendations.

Just thinking about this some more, if it's sat that long, I'd be more concerned about the brake fluid and coolant than the diff fluids.

 

I would expect voltage to be over 14 volts after a start, so you may have an alternator that is on the way out