I'd start with a paint cleaner, then a clay bar, then a polish and finally a wax. I don't like to cut until I sell it. You'll find it will come up ok. Buy a random orbital sander otherwise your arms will get sore.
Most of the scratches will be in the clear coat rather than the colour. Using the clay bar to smooth the paint out is a start. When you use the polish do it in a circular motion as this will fill in the scratches. Whereas the wax should go on/off the way the ait flows over the car.
Let me know if you have any more questions. I used to spend a whole weekend polishing my Audi by hand, as I have said before I am a little OCD