Over thinking, no. Planning ahead, yes.
We have not had a puppy in the house in many years, only older dogs. Introducing the new dog to the one already at home turned out to be really easy. We have an empty lot next door and introductions were done there. Walking them together is a great idea too. In fact, when we got Melody and Archie, we actually too Potion and Mardi with us to meet the new member. The rides home were amazingly easy and quiet.
As far as meeting other human family members, again outside, taking a walk, talking to them, lots of interaction.
Inside, close monitoring but letting them explore and sniff. Meal times very closely monitored. Mardi and Archie eat at opposite ends of the kitchen and I stand in between. That's because Mardi always finishes first and tries to hone in on Archie. I DO NOT ALLOW that. Treating has to be carefully approached since they most likely will be standing/sitting next to each other.
Also, the pup at home always gets fed/treated first, in or out the door first. They were the first set of brown eyes in the house and I enforce the "chain of command". That can change later but to begin with, it averts competition and they know I am the one who sets the rules.
If the new dog is not housebroken, start with potty training 101. They have the ability to "hold it" unlike a puppy, they just need to be shown where it is appropriate to go. You need to discover their signal. I do believe having another dog already tuned into potty manners helps the new dog; doggy see, doggy do.
Toys and play times need to be monitored so they can sort out what is appropriate and there is no competition.
Think you might be surprised how easy it can be especially if the new family member is going to be a lab.