Which is the best approach to "suspend" the activity of a whole AOG cluster thinking on start it again later?
You don't need to suspend data movement, but otherwise what you've written for option #1 is a good approach!  Before doing anything, I would disable automatic failovers on all replicas, to prevent any unexpected failovers when you bring the AG back up.
Then, as you said, shut down the secondaries first, then shut down the primary.
When you bring the primary back up, it should come online as the primary again.  Then bring up the secondaries.
Make sure to turn automatic failovers back on once everything is stable, if you had it on in the first place.