I have tried clay bars,the trick is to get a lot of the cleaning fluid on it so the clay bat slides easily over the surface, also be careful to not drop it or it will pick up dirt and scratch the car.
But for a cheap way to renovate the paint try using ice. Two years ago my son bought a car that had been sitting in a backyard for a few years, it had lots of dirt and lots of nasty black dots that just wouldn't wash off. I read about ice so got a large ice block from the freezer, gently rubbed it over that paint work and as the ice melts you can rub it faster. All the nasty dirt came off better than a clay bar and if you drop it on the ground you can go to the freezer to get another block of ice. Since then I have used ice one all my cars before polishing them and very happy with the results.
