I want to

- specify which websites may store cookies/cache. All websites not specified can not store anything (and thus not track me), and all data for these websites is deleted once i close the tab

- i want to remember all my history

I can do this in Firefox on macOS (with some container extensions, can’t remember the names now)

I started using the DuckDuckGo app on iOS to do exactly this. You can choose to "fireproof" any site you're on, adding it to a list of sites that's immune to clearing all data.

I don't think it has a history feature at all though.

That’s pretty cool, i’ll check it out.

Unfortunately you can’t change ‘Font size’ at all in the Duckduckgo browser.

Safari used to have a feature where you could delete all cookies except for ones you had explicitly marked to keep. So, for example, I might keep ones like my bank login name and my amazon history, but very easily remove everything else. I used this all the time. Even better would be the option to delete all but selected cookies every time I closed Safari.

I assume you are talking about macOS, not iOS.

On macOS, there's also an app to achieve that, called "Cookie": https://apps.apple.com/nl/app/cookie/id1473091386?l=en&mt=12

On iOS however, Apple's walled garden...