First, congrats on the kid.
Secondly, its polar opposites of workout to lose weight and gain muscle.
I have some general rules of thumb, depends on your body, genetics and general habits as well as what you are prepared to do.
To lose weight is diet dependent thing. Unless you're like my wife who lives off candy and doesnt gain a pound, unlike me who gains 20 lbs just looking at a cake the wrong way.
Less CALORIES is the solution. None of those other diets work, and if they do, it was simply putting them in a caloric deficit and they didn't know it.
To gain muscle, you want to be in a caloric surplus, roughly 250-350 calories over your daily intake for your weight.
High intensity workouts are good for burning fat, working out with a slower heart rate is burning fewer calories.
For muscle gain its the opposite, but after the first year, or less, you'll hit that plateau. So I recommend doing the twice a week splits per muscle group after the first 3 months of getting back into it, focusing on compound movements. Dbal helps too.