Put the shammy in the bin.
Get a proper drying towl which will do a far better job of drying the car such as the SONUS ones Rich was talking about, see above. The buffer you are talking about... Most people tend to "buff" off by hand with a good quality Microfibre, and use a PC (machine) for removing applying polish to remove swirls, scratches etc and give the paint some nourishment...
Even wax, I prefer to do by hand rather than via PC.
A nice easy start would be.
Wash with the 2 bucket method using a lambs wool wash mit.
Dry using a Waffle Weave Drying Towel.
Polish a good off the shelf product such as Autoglym SRP
Seal with Autoglym EGP
and top up with a nice wax, such as Natty's blue, P21s, Chemical guys XXX, etc...
Perhaps look at some tire gel and trim detail products to complete the overall look of the car.
Thomas