If you've got the space, make a list of the larger chips and any part that catches your eye on each board, number the back of each board with a marker pen so you have a board ID for the list, and if possible note on the list what the board is out of and what the fault was, then store them without stripping the parts.
Reason: Many of the parts will need support components e.g an oscillator crystal for a MCU that are already conveniently grouped on the board. If you strip the parts before you need them, it costs you time and money (due to wear and tear on your desoldering equipment), support components are likely to be missed or get lost and the chances of it sitting in a draw gathering dust till your estate sale
* are >90%
However you do need to limit your scrap board storage to avoid falling into the pitfall of hoarding. e.g. one box for 'virgin' boards, and one for partially stripped boards. When a box is full nothing more gets kept until you make space for it. When a board has had most of the nice stuff stripped, or you need the space, be ruthless and dispose of it as eWaste. (Possibly after salvaging any remaining high value parts that you anticipate using within a year)
* Don't leave your friends/relatives/executor the task of finding good homes for a collection like this:
https://www.eevblog.com/2015/04/26/eevblog-737-worlds-biggest-collection-of-electronics-components/