The first few days in your new house will feel just as if you're still packing – just you'll be unpacking and making a mess. Its impractical to even try to consider being organized and unpacked within one day, unless you have very few belongings, so you should try to unpack in the order you packed, or as close to it as possible – placing boxes in or near the room you're planning to unpack may be impractical, depending on the size of the house, but makes things easier.
Its perfectly acceptable not to unpack everything in the first few days – if you've moved to a new area, you may want to (or need to) explore and familiarize yourself with any public transport, local facilities, or shops in the area. You'll need to go out and buy at least the basics – saving the 'big shop' until you've unpacked your kitchen. You'll probably unpack that and your living room, and if you're not taking long off work, your home office first.
Unpacking takes place over six to twelve weeks, depending on your family, and you may find that you have to permanently store items in a garage, basement or attic, because there just isn't the room for them.
Most of your utilities should be on and connected for moving – but you may find that your Internet and phone, cable or satellite take several weeks to be reconnected. In these cases, you should make the most of the change, and unpack as much as you can. After a month or two, your life will be back into its work/life/sleep pattern so consider any break from it, if you can, a holiday of sorts. Once your utilities are all reconnected, you may find you have less time to unpack, so its good to get as much of it out of the way as possible.
If you are returning to work, outside the home, after a move, ensure you know your new route to work, and allow some extra time for the journey....just in case.