Hello personally I would reccomend meguars ultimate compound, Polish and wax and a paxk of applicators. Regarding the black dots try a bug and tar remover. Give the car a thorough wash using a mitt and two bucket technique. I would also reccomend clay baring the car before compound and so on. Your probably looking at £60-80 of products listed there but they will last a while and achieve great results.
Other members will also give you other ideas and products but remember its all based on personal preference.
In my opinion meguiars is cost effective does the job and you cant damage your paintwork. Get some pictures of the car and paint on here so we cab see the damage and inperfections.
Regards shaun