People talk about kids having trouble with phones. That’s true. But parents have trouble with phones too. Maybe worse. Try having a spot to dump your phone when you walk in the door, and don’t pick it up again until after the kid goes to bed.
Have fun with your kids - like laugh out loud, roll on the floor, fun. Tell jokes, play pranks (on grandparents is the best), have inside jokes, see the world their way. It can start early. They pick up on it really fast.
They are wiring their neural networks constantly, from the instant they come out. (Before, actually.) So you are wiring their brains through your interaction with them, your interaction with others, and what you expose them too. Which means they have to be stimulated, the right amount, to the right things. (Within a broad range, of course.) Make sure they’re safe, secure, but challenged.
Kids find being indoors simultaneously boring and overstimulating. (I do too, actually.) Get outside as much as you can.
Bad behavior is often the result of not having enough responsibility/freedom/challenge. Close cousin to being bored. Like anyone, kids are happy when they have responsibilities, but ones that can fulfill well. It’s harder to teach responsibility than to just do the task for the child. If theres a behavioral issue, often it takes stepping back and thinking about how the child can undertake more responsibility/freedom, teach that responsibility/how to fulfill the duty, and let them take it from there.
The advice about postpartum depression is really good and critical. Your wife has just completed an endurance event that far exceeds anything you can and would ever do. And her hormone-producing organ just fell from her body, she has to start over *and* feed a tiny glutton on very little sleep. It will take 3-5 years to get back to where she was beforehand. (And won’t ever truly get back there.) And, that whole time, the way you treat her will be part of how that baby’s neurons develop. It’s time to buckle down and learn what being a real man is all about: true service to others. You have to take care of yourself - eat well, exercise, etc - but you’ll have to strip away a bunch of other nonessential things. There’s nothing easy about it, but that’s what makes you grow. (We’re not so different from children, as you’ll come to find out. Same needs, different manifestations.)
Good luck and have fun!