Doing it myself, I'd try with the least abrasive product/technique 1st. Since your car was recently painted, we would hope that there clear is new and still thick.
Anyways, I'd start with a wool pad, 3M Rubbing compound, and a buffer/policher... not one of them super high-speed ones either. Your routine buffing/polishing orbital buffer type thing (~$20). Keep in mind that if you don't have this stuff already, it will cost a bunch and the body shop may charge about the same and guarantee the results.
Do that for awhile... Slight progress? Good progress? If slight or poor progress, after a loooong time (20 minutes in one area), then wetsanding will be the next step.
There is a technique to doing this. If you have not done it before, or aren't being supervised by someone who has, you are risking paint damage that the body shop may not be able to easily fix. STOP HERE, take it to the shop.
Read up on wetsanding tips, gotchas, and process/technique... even if you've done this before.
Then just go from most abrasive, to least. Each time further bringing out the shine and reducing the scratches to nothing.
The higher the grit, the better. You will easily find 2000 grit wetsand paper at the auto parts. Look for and get 2500 grit. It's slightly less abrassive than the 2000 grit.
After evenly wetsanding the bad paint off, you will use the rubbing compound, to eventually polish and a really good wax (I used to use Megauiar's).
Please read up before you follow my steps. they are definitely not detailed enough and you could FUBAR things in a worse way.
Good luck!