Are there any GPS data pusher for Arduino?
Check this shield out, it sounds almost exactly like what you need, plus it has OBD2 (CAN) access to log RPM, indicated speed, steering wheel angle, and whatever else your car exposes. You can get a GPS module from Sparkfun as well. Matter of fact, I'm using it in a very similar project, but development is paused until I upgrade to a Mega, since I've run out of RAM.



The shield comes with example code that's hacked together from other sources but it serves the demo purpose well.

As for pushing to a server--that'd be tougher. I would go the route of a Bluetooth shield and make a corresponding app for the phone that pushes the data.