Both me and my husband have never, ever lived in a house. That’s how it goes when you are a born and bred New Yorker. Hopefully by May, we will be living in our very own little house. Last night we started listing the things we’ll need that we never, ever thought to buy before. Our very short list:
Then our imaginations failed us. What else would a home owner need that apartment dwellers don’t?
A Dog.
The Home Depot 1-2-3 Home Repair Guide.
Congratulations on becoming a home owner. It is very different, but it will give you a sense of enjoyment.
What kind of property is it? Is it a rowhouse or a single family detached house? Does it have a yard? How big? Is it grass? If so, you may want to purchase a lawn mower of some description.
Are you going to paint any of the rooms? Now that the place is yours, you can. You might want to invest in a few tools as well.
Good Luck!
Adding in on Edit:
I didn’t see this the first time, but I second this recommendation. Even if you don’t do it yourself and hire someone, it is great to know what they are supposed to be doing. I’ve saved money and gotten ideas on what I wanted done, from reading this.
I’m laughing a little because I had all of those things when I lived in apartments (I have a serious gardening problem.)
In addition, in no particular order:
I’m sure that there’s more but I’m blanking out…
Possibly a lawn mower (unless you can get a kid to do it for you).
Ice melt.
Duct tape.
Prolly a light-duty wheelbarrow (optional, but handy).
A basic toolbox (hammer, screwdrivers, pliers, wrench, screws and nails).
Buckets.
It’s a detached neo-colonial (so it’s older) with a back yard with grass and a patio-- and a shed and black top for the car.
A home repair guide-- excellent!
Some light gardening tools–a trowel and a gardening fork. If you’re concerned about comfort, knee pads and gardening gloves. If you have anything to edge, then something to do the edging with–one of those ninja stars on a long handle. I have no idea what they’re called 
Also, a jug of Home Defense, assuming that you don’t suffer insects gladly.
Power outage supplies (outages are way more common in houses, in my experience): lots of candles, a lighter, and a battery-powered radio.
The first thing I bought after my house was a shed. Gotta put the lawnmower et al somewhere.
A crafting room.
A weed-whacker for those parts of the lawn close to the fence that the lawn mower won’t get.
Hedge clippers might be useful to have and maybe a push broom or heavy duty outside broom.
If you live in a part of the country where winter occurs, you’ll need a snow shovel. Not until next winter, of course, but you may find them in “winter clearout” sales now.
If there’s a Lowe’s nearby, go to this site and get a 10% off coupon. Good up to $5,000.
Home Depot also offers one but I don 't have the link handy.
Find the local hardware story. Not the Home Depot, but the Ace or something like that, that has been in business for about 50 years. That’s the kind of store you can walk into, say “My faucet is making funny noices that sound like …” and they can help you get what you need to repair it.
That and a good home repair book (I also like the Home Depot 1-2-3). Everything else you can pick up when you need it.
And be sure to get an Ace Card. I can’t believe how often they send me coupons/etc that I actually use!
One of my standard housewarming gifts for my friends has been a nicely wrapped and beribboned Plumbing Emergency Pack containing a good toilet plunger (splurge on the really good $7 one, not the crappy $2 model, this is not the place to cut corners), a plumber’s snake (also an inexpensive item) and a packet of Rubbermaid yellow gloves.
I dunno if you are used to having a landlord or maintenance guy on call to handle that stuff but if so, keep in mind that you are now your own “Housing 911” so if you don’t have those things onhand, buy 'em. Like a fire extinguisher it’s the sort of thing that when you need it you need it right that instant, no time to rush to the store.
Regarding an edger (what Sattua was talking about), I bought a nice “manual” one thinking I’d be all green and so on, and I immediately regretted the decision. It just doesn’t work very well, if you have to do yardwork get yourself a good electric weedwhacker (again, don’t get the cheap $20 version, a relatively top of the line model is maybe $70 and the difference is incredible). This will also handle mowing a small lawn (although it’s not as good for that as an actual lawnmower).
Also third the recommendation of a good homeowner’s repair book like the HD1-2-3.
That’s exactly what I was going to say. Home Depot, Lowes are great when you know exactly what you need, 8 sheets of 4x8 plywood, or a reciprocating saw or what ever.
But for the “This little doohickey fell off my 60 year old whatsahoozit, I think need a new one” type questions find some 180 year old guy puttering in an old hardware store, preferably one that has noticably expanded over the years.
I use my SUV more than the other tools. You will see why they are popular despit e the bad rap.
A mdeium sized tool set. You can buy sets in many different sizes for reasonable amounts of money. Don’t buy the cheapest one though. A hammer, pliers, a few wrenches, and a socket set are needed at a minimum.
a push broom
Garbage bags
yard shoes - for just going down to get the mail, or chase the neighbor’s cat off your lawn!
a nozzle for that hose
You may want to get a push mower or an electric mower as opposed to a gas powered lawn mower depending on the size of the lawn.