smoke detectors
carbon monoxide detectors
first aid kit
toilet plunger, toilet snake, etc
duct tape, electrical tape, cable ties
spare light bulbs
cleaning supplies such as brooms, mops, buckets, sponges, etc
snow shovels (if you live in a climate that gets snow), along with ice chopper, deicer,tarps,etc
garden hoses, water buckets, trash cans
good sturdy ladder (for cleaning leaves out of gutters, checking roof, cleaning chimney if needed!)
wheel barrel to make yard chores easier, garden gloves, if you have or plan to do landscaping....potting soils, mulch, hand tools, etc
humidifiers,dehumidifiers
When you move in..try and get the names/numbers of good electricians,plumbers, mechanics etc...you never know when you will need them ! (this one's from experience..first week in our new house the sewer line clogged and we had to get a plumber!)
Those are just off the top of my head..but I am sure a lot more DIS'ers will be along with helpful hints and advice
Good luck in your first/new home!