I do detailing on the side so I've got lots of experience with this. Firstly, you DO NOT want to hand polish a car. To give you an idea of how much work you'd be putting in doing it by hand, it takes me on average about 6-7 hours to wash, claybar, polish, and wax a car. You will need to claybar the car before polishing as well in order to remove any extra contaminants, otherwise you'll be soiling your polishing pads with dirt that wasn't removed.
I personally charge about $160 for cars and just add $30 for larger vehicles (includes wash, claybar, polish, wax) although you may find others who do it for more or less. Beware of places that don't charge much as they may cause more damage to your paint by using rotary buffers with dirty pads. Also, I wouldn't recommend going to a dealership to have polishing done. They focus on making money more than anything.
Just my 2 cents. If you have any other questions for me or are interested in the services I personally offer drop me a PM. I don't hold any detailing knowledge back even if you're not a customer of mine.
Wax will only mask swirls, not remove them.
EDIT:
On a side note why the hell was a year+ old thread revived?