Placeholder....
If your looking for a system that "(has) amnesia" doesn't store your internet history on a physical drive, doesn't allow sites to track you, and even anonymizes your internet connection, then you might be interested in Tails:
https://tails.boum.org/
Sound too good to be true?
Maybe so!
Tails loads a virtual drive into your RAM (RAMDRIVE for you old school DOS users).
In spite of multiple security flaws, if used correctly; Tails may by far be the best way to remain anonymous on the internet.
Correct usage would require connecting to Free WiFi Hotspots at your favorite (or not so favorite) restaurant, motel, hospital, etc... as you avoid using the same Hotspots at routine times.
In other words... be unpredictable!
Don't use the same WiFi Hotspots at the same times.
Shuffle it around. Avoid an easy to follow schedule of habits.
Just remember that you can't keep anything that you download and/or install during a Tails session... it has "amnesia".
There are other systems up for consideration here, and I personally don't like the inability to keep downloads and installed apps at the end of a Tails session.
So I will be listing some other Free systems here as I get the chance to try and evaluate them.
over and out for now?