Getting your breathing right is important on main lifts.
On isolation lifts not so much but still it’s good to develop good habits.
When going for a main lift the breathing is actually part of the set up. You need to get it right every single time. It becomes part of the lift.
If I walk up to a heavy deadlift I want to make sure my core is going to stay as tight as possible. How does this happen? Well once I have made a good position on the bar and have pushed my chest out as far as possible I am going to breath in a huge amount of air into my belly and hold it. I am going to squeeze my abs at the same time and this will maintain a strong core position.
When wearing a belt you actually push your abs into the belt. That is the purpose of the belt. You hold your air in until the top of the lift. This creates tension through the body and a solid core. It’s also the safest way you can lift.
I used deadlift as an example but this is the same for a squat or a bench press. Actually on bench press some lifters will hold their air in for a few reps. I don’t advise this for new lifters but just giving you an example of how holding in air can help build a solid core.
As far as whether it’s your nose or your mouth that is totally irrelevant and not worth worrying about.
In my opinion new lifters worry too much about breathing on isolation exercises when really your body will do it naturally.
If you went to pick up a washing machine you aren’t going to be thinking, how do I breathe for this. You’re going to be thinking, I hope I don’t break my freaking back. You will naturally suck in a huge amount of air and you will hold it until you get it up.