Polish : will polish off a thin layer of clear coat, to remove swirl marks, fine scratches, and to bring back gloss.

Wax : add protection layer to the paint to protect the clear coat, looks glossy, and water beading effect.

Coating : permanent sort of thing similar to wax (depends on brand), will look gloss & shine providing you wash frequently. Wax can be added occasionally to further enhance the gloss & water beading. Coated car not to be polished otherwise will tear off the coat, so eventually you will have swirl marks, water marks, etc. Can’t prevent stone chips.

PPF : self healing good type will self cure after stone chips, may look different color if wrap only front part. May require special care during wash. No more polishing. Wax I’m not sure.

Best, if budget allows,
Coating first, then wrap with PPF.
And followed with recommended maintenance by detailing shop that do the PPF.