I use Firefox with privacy badger, uBlock, and IronVest. I also have it set to disable 3rd party cookies. Sometimes 1st party cookies are necessary to interact with a site but if I’m not interacting (I clicked a link and view a single page) I get no cookies.

I’m not sure how to prevent saving in the first place, but you can use the Cookie Autodelete addon to remove them as soon as you close that tab.

just disable all cookies and make exemptions for some