I purge kegs occasionally such as for a beer I want to preserve the super hoppy character, but I don't bother most of the time. I do purge the headspace immediately after filling and putting the lid on the keg, after racking the beer from the fermenter to the keg.
I just remove the QD, run a paper towel dipped in Star San up and down the gas hose and fitting, and put it down into the keg.
I've never purged beer bottles, but I do use o2 scouring bottle caps.