The big man has pretty much covered it but I wouldn't go more fine than 800 grit silicon carbide (wet n dry) if coating on top as you need somthing for the paint to adhere too. Also I wouldn't use White Spirit either as there is too much room for contaminates and getting a paint reaction even if washed down with soap and water after the White Spirit. Either use Soap and water, a bit fairy will do or use an IPA (Isopropyl alcohol) solution or wipe or dedicated painters wipe / panel wipe between coats. That's being really fussy though. Soapy water is good enough but make sure it's totaly dry before coating and you may want to give it a quick wipe over with a tac rag to get rid of any dust particles right before coating.
Depending on how deep the scratches are you may get away without painting. Has it gone through the clearcoat? In other words have they gone through to the colour so a compounding solution (T Cut) wont work. I wouldnt use T cut as it's aggressive but maybe some G3 Scratch remover might work. You'd be suprised what can be done with a bit of polish. I'm sure you remember the T Cut days.
Otherwise it's painting......
Rub down the area well with some course wet n dry heavier to start 240 / 180 (dry).
Fill and rub down to a 400 grade (dry) finish including rubbing down some of the surrounding area.
Fill again to get the last little niggles and perfect. Rub down to a 400 grade (dry)
Prime
Rub down with 400 (wet)
Apply 2 coats of basecoat or untill covered and rub down wth 400 or 800 (wet)
Apply clearcoat 2 good coats should be enough but allow to dry between coats and rub down with 800 (wet) and for the final coat once cured, 24 hours, 1200 / 1500 (wet) to get rid of the Orange peel and then polish back up to a high shine.
If you do end up with the odd run, don't worry. Allow to dry and use a flat blade to scrape the high points off and the rubbing down will get rid of the rest. Use a block if rubbing down a flat surface. You will find that as you go through the coats it will look better and better and your spraying technique will improve. So hopefully by the time you get to the laquer which is more difficult you will be OK. Try not to apply too thick, light coats back and fourth. Many light coats is better than one thick coat, start with a light dust coat before working you way up to a thicker coat and allow 10mins to flash off in-between if the same layer and allow longer if jumping from primer to base to clear. Cover the surrounding area too as when you polish this will all blend in together. Just remember you can't screw up the spraying as all you need to do is rub it back down, try again and give it another coat.
Watch some youtube vids to get an idea but you will find various techniques and grades of scratch folk use.
This probably wont help you but if you want to see how the pro's do it...
https://www.youtube.com/user/MrZoeystevenson
