Washing, polishing and waxing are completely different processes which achieve separate aims.
Washing, usually with an automotive shampoo, removes grit and dirt.
Some automotive detergents are water repellent when dried.
Polish removes grime from paintwork using very fine abrasives in the polish.
Any automotive polish will brighten paintwork and leave a good shine.
Waxing is a final stage in the cleaning process.
A good quality automotive wax will seal paintwork to preserve the shine and to protect the paintwork.
After washing and if necessary polishing two or three applications of automotive wax per year will render further polishing unnecessary, washing will restore the shine.
Carnauba wax is said to be the best and longest lasting automotive wax but it can be difficult to apply in cold weather and doesn't give good results if applied in warm sunlight.
Other automotive sealants such as Auto Glym protect the paintwork using polymers instead of wax.
Polymer sealants are less expensive, easier to apply but have to be applied more often.
Good intermediate products for use between wax applications are automotive glazes, easy to apply and with superb end results. I use Pre Amigo glaze, difficult to get hold of in the UK but well worth the effort.