You have a dilemma many of us are in but I wouldn't so much have a potty box setup.
I DO like your idea of the larger cage with the pee pads in it so there is easy cleanup. But not really to TEACH the puppy to go in the house. So, at night, I'd see if I could borrow a much smaller crate to keep beside the bed, set the alarm for 2 am to take the puppy out, then sleep the rest of the night. With a smaller crate and NO pee pad then the puppy will start to learn to 'hold it'.
Then during the day when you have to be gone 8 hours or so, I'd use the much larger crate. That way, if there is an accident, the pads will absorb it for cleanup but so would any other towel you'd stick in. There will be room for the puppy to stay dry on the other side of this larger crate.
When you are home there is NO NEED FOR ANY BOX. You don't want to 'teach' him to go in the house anywhere. Instead, when you are home you take him out about every hour or so to do the housebreaking where you WANT him to 'go' outside in the yard. Get those babygates up and close the doors to the rooms you don't want him to go into. And then you need to pay attention because any 'accident's are then YOUR fault and all punishment must be put on YOUR head not the puppy!
Good luck! Large crate with pee pads in part of it for when you have to be gone for a long time. Otherwise the tiny crate to help teach the housebreaking (at night or when you are gone for a few hours) and then NO crate when you are home.
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there is great information