Congrats on the parenthood!
As for Argento, there's a few I haven't seen yet but the quality of his work is allllll over the place. You definitely want to stick with his 70s and 80s films.
Also, are you looking for more supernatural/fantasy kind of stuff like Suspiria or more grounded?
For supernatural, Suspiria is actually the first part of his 'The Three Mothers' trilogy, followed by Inferno and The Mother of Tears. I haven't seen either of those because I've heard mixed things about Inferno and Mother of Tears is pretty universally disliked. I can't comment if you should seek them out or not. Phenomena's pretty good, but also pretty crazy.
For grounded stuff, I'm a big fan of his gialli. They're almost all excellent. Tenebre and Deep Red being my favourites. The rest of his gialli never hit the same heights as those two, but I think they're all worth checking out, even the lesser ones like The Card Player and Do You Like Hitchcock? Just be aware some are more straight up thrillers and shouldn't be considered horror.
If you dig Argento's style, you should look into Michele Soavi's films as well if you haven't already seen them. He worked under Argento for many years and shares a similar sense of style. I highly recommend Cemetery Man (aka Dellamorte Dellamore) and StageFright: Aquarius.