Your graphics card will make very little difference in how Premiere Elements performs. I'd recommend that you get an ATI or nVidia card rather than Intel graphics. But other than that, virtually any off-the-shelf card will do.
As far as your other hardware, I'd recommend at least a quad core i5 for 6 gigs of RAM and at least 500 gigs of hard drive space. (Desktops are better than laptops as far as editing performance.)
I've run the program on both a Windows 7 and a Windows 8 machine and it runs great for me on both.
PC I built for my wife http://www.pacifier.com/~jtsmith/ADOBE.HTM would do very well for Premiere Elements
This is, of course, MY idea about what to build, if I was building a new computer for Premiere Elements... YOUR ideas may wind up being different
Wish you could build a computer like that for me, John! How much did that one cost you?