One type of polish isn't enough to make it look as new as you would like.
If it's quite bad, I suggest using a stage 1 cut n polish to remove dirt and grub on the surface. After that you use a wax polish to further cut down the grub to nothing.
You will know if your paint is good when you run your whole hand across the surface. If you feel tiny tiny little sand pieces, it means its still got crap on the surface.
Mind you, I spent 20+ full on hours polishing my DC5R and now, the surface is like silk when you run your hand across. Also every fine scratch there ever was, isnt there anymore. I'm lucky because there wasn't even 1 small dent on the car, so now its better than showroom grade.
By doing a good 20hrs, you also have the benefit of maximum protection against dust, dirt and EXTREME water beading on your paint! Makes your car water proof. Oh, also you'll get sore arms and fingers for a while.
I haven't washed my DC5R for about 3-4 months now. Simply because its still so damn clean. Dirt, rain, crap all just flys off the surface.
I used KITTEN products.
-Liquid cut n polish 1
-Liquid wax n polish
These products are very mild and the Liquid wax n polish is SUPER mild yet works so well in removing tiny sand like crap WITHOUT SCRATCHING the paint no matter how hard you push. I pushed and rubbed the crap out of it and not even 1 scratch appeared.
I've tried others but nothing creates shine and removes fine scratches like this.
And also tried full range of Meguires, Auto Glym, etc. But nothing comes close. Technique is the key element in polishing.