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Buy spare parts for the AC / furnace / water heater. Caps, contactors, ingnitors, flame sensors, temp switches, filters, anode rods. Clean the dryer vent. Check the condensate drains, backups. Plug in a lamp to every outlet to check function, tightness. Flip every switch to listen for crackling.
Just the basics...
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This, except you should get a real outlet tester and a multi meter and test all the outlets.
Plus
Have or do all the drain lines in the house along with the sink traps. Find and test all the water shut offs, make sure to lable and tell the wife and kids about them. Check out the main water shut off, clean out the box and test the valve. Then store the tool somewhere it's easy to find and get to in an emergency. Same thing with any gas lines.
If you have hardwood floors or know you'll want to change flooring or do anything that involves drywall do it before you move anything into the house.
I personally thinks it's a good idea to live in the house for a bit before you start planning for any remodeling. The way you think you'll use and live in the house may be different that the way you actually will. Once you have a list plan it out in a logical way so you'll save money and time not having to redo or cut into something you've already finished.