Tammy, this is what I got from HP "The drivers for your HP product are already included in the new Windows 7 operating system! You do not need to download drivers to use the product . Simply connect the printer to your computer with a USB cable, and Windows Update automatically installs the driver for your product." This here will tell you how to proceed with the installation of your printer. Hope this helps, good luck.
It will work, but you will lose most of the utilities with Windows 7. However, you do get the essential tools with the Microsoft drivers. If you want the full tool set, use a standaloone XP machine you keep offline. It probably won't install on Win7 due to age.
However, you may have a fighting chance with 32-bit Win7. But assume no for 64-bit. You can find the XP driver here for the full toolbox set. I doubt HP wrote Vista drivers for this. Even if they did, I wouldn't be shocked if they never wrote Vista 64 drivers. This was a very common issue back then.
If this gives you problems, don't bother. It will probably not work whatsoever.