As with others, showers are free as part of lounge access I pay for separately (either DL SkyClub or Centurion Lounges via AMEX Plat or AC via Citi Prestige until benefit disappears). I don't pay for it because of the showers but having access to them is an added benefit. For me the preferred order is shower and then food / drink but sometimes due to the wait for a shower it goes food / drink and then shower.

There are four situations where I consider showers a must:

1) Full day of work / play / touristing and going straight to the airport for a long-haul or transcon. Got to shower and get out of those work clothes or sweaty play clothes and into something comfortable

2) Post red eye of any sort whether connecting or terminating

3) Post long-haul before connecting to short-haul

4) Post transcon / medium-haul before connecting to long-haul (e.g., RDU - SFO - SYD) though this one is more of a nice to do if I have time and not a must do as with the prior 3