Safari is a web browswer and cannot be formatted.
The very best thing you can do is to use the RESTORE disks that came with the machine, assuming that the Restore disks are for OS X (later than 10.1) and restore the machine the the condition it was in when you first took it out of the box.
Failing that, using the OS X installation disks, you perform a Format and Install on the machine. This will destroy ALL the data currently on the HD and install a new copy of whatever OS the installation disks are for. Bear in mind that iLife is NOT part of the installation after 10.2
If the Restore disks have iTunes, iPhoto, iMovie and iDVD on them, you could restore from those disks and then upgrade the OS using whatever later installation disks you have.
Private browsing is a function of Safari where nothing is left in the History section. History and any cookies that were installed during the Private Browsing session, are deleted on exit.
You can always delete the History and all the Cookies within Safari.
I am in the process of giving away an Ibook to a collegeheaded relative and will probably do the same sometime later with my tower. These machines may end up in a dormroom with a bunch of techies. Is there a way, short of reformatting to eliminate all my history with the machines so that I can hand them over as virginal as I received them. How thorough is reformatting Safari? It sounds like it will take care of some of what I am concerned about. What, by the way, is Private Browsing all about? Does anyone understand it thoroughly?