Congratulations. After opening the box and making sure the machine is not damaged, you have the correct next step, checking the inside. After that and hooking up the machine to a monitor, keyboard and mouse only, you should go ahead and start the machine.
My personal practice is then to clone the system disc onto another of equal or greater size. That way, if for some reason, I really muck it up, I can always go back to the original. I used to use Ghost, but it has not kept up with new developments. It works fine with XP and IDE drives, but SATA drives and Vista are not properly supported. I now use Acronis True Image 10. It can be used to back up, but for me the most valuable feather is the clonning feature. Others can back up, but clonning seems to either be an ignored feature or one to difficult to put in run-of-the-mill backup programs.
Acronis True Image 10 is available as a CD from Newegg for $35 including 3 day shipping or $20 for the downloaded version. Either version will require you to print the manual, and the downloaded version will require you to burn the recovery CD.
I know it's tempting to just jump in, but pace yourself, and you will be rewarded in the end. I also bought a book called "Windows Vista - The Missing Manual" The primary author is David Pogue and it is published by O'Reilly Press. I found their book on W2K, XP, and XP SP2 books most helpful, so I bought the Vista book before I started.
Vista is SIGNIFICANTLY different from XP. All the XP features are there along with some new ones, but they are in different places. Many items are easier, mapping a network drive is done in about half the steps.
After you have Vista up and running and backed up/clonned, then you can start installing the printers and other periphials.If you have an older printer or scanner, you may be in for a disappointment Check the manufacturer website for updated drivers. Some drivers may already be on the Vista installation.
Some seem to have a problem with Vista, but I have found it to be an enjoyable, smooth and stable operating system. The graphics are fantastic. You did not indicate whether you are also getting a new monitor with your new machine. A higher resolution monitor will really show off Vista to its best effect.