The key French press cleaning trick is a _fine_ kitchen sieve, not too small, at least 3" wide:

Pull out the French press plunger, add water and drain the resulting mud through the sieve.

A normal small 2" coffee sieve is too small in diameter, it will clog.

The 3" (4" is better, especially for the larger 1L press) allows the water to pass in a fast pour. And make sure it's a fine sieve, so the grinds stay in.

The grinds mud then goes from the sieve straight to trash.

In store the sieve at the sink with the other cleaning utensils. In direct access storage, so to speak, a local cache even.

Well if there's one thing I hate cleaning more than a French press it's a sieve! Or do you have a sieve specifically for the press? That seems like a good idea.

That’s funny. When I worked with Italians and I wanted them to teach me Italian swear words I’d ask them about French coffee. :D

Personally I like both but mainly drink espresso.

I’ve also got an AeroPress I used for years before I got the espresso maker. I still like it but it’s coffee is nothing like espresso.

why would you take care to NOT get coffee grounds into the sink/drain? Its a feature, the grounds remove some of that fat/etc. that builds up in any kitchen sink/drain.

I myself just wash out my French press with water and let all of that go down the drain, makes it the easiest to clean. Not to mention there is no need for onetime filters like with many other methods (same for Bialettis/espresso maker)