Whenever you move into a new home, the first thing you should do is give it a thorough cleaning. No if ands or buts about it. If you find that for whatever reasons, you haven't had a chance to do a thorough cleaning before your things arrive at your new home; it is still possible to do one by cleaning around your belongings. Not the perfect clean you may have been looking for, but nevertheless a good cleanup. All you need is time and a little patience.
Next, brace yourself and look inside the oven. If you need to, apply an oven-cleaner. Most take about 20 minutes to fully work. This gives you time to do the rest of the stove.
Make sure you clean under the hood and use a grease-remover if you find the regular cleaner isn't getting off the tough stuff. It's not a bad idea to place a sheet of brown paper beneath your work space to collect any drips that might fall.
Once you've thoroughly cleaned the top and front of the stove, remove it from the wall and clean underneath it. If you can, also clean the sides, along with the front panel and temperature dials.
Now it's time to tackle the refrigerator. If the previous owners have any sense at all it's been cleaned out, but that doesn't mean it's sanitary. You still need to clean it well, including removing the drawers and bins and washing them. Wash the inside wall and shelves, removing anything that can be removed and washing it separately in the sink.
Check the freezer. If the refrigerator has been unplugged, wipe down the inside or clean it thoroughly if it needs it. In case the refrigerator hasn't been unplugged, you should unplug it and let it warm up before you attempt to clean it. This will make it easier to clean. Also, make sure you use a soft cloth to avoid scratching the surface.
Move the refrigerator out from the wall and clean behind it, then on top and the sides too. Dust and dirt also gathers on handles and along the plastic sealing that encases the doors.
Clean the top of cabinets, and cabinet doors. If the surface is wood, use a wood cleaner or a mild soap. For grease-stains, use baking soda and water. Make a paste and apply it, letting it sit for a few minutes. Also clean handles and inside drawers.
Counters usually require less work, just be certain you clean between cracks using a putty knife to remove any debris. Clean back-splashes with a mild cleaner or baking soda and water.
For wood floors, sweep the floor well, making sure to clean under heating vents and under appliances. Use a mild soap to clean the surface of the floor.