Depending on the colour or color, t cut can be a bit harsh. Try Scratch X, a lot milder and works very well. Get it from halfrauds around £9. Wax over it afterwards to reseal the paintwork
I recommend a microfiber cloth specifically. These have a much less tendency to scratch your paint. They can be picked up at most auto parts stores and washed and dried gently in your washing machine/dryer.Second that but use a lint free cloth or you'll put scratches on as you polish them out. Good luck.