Hi MatCreator,
Your render settings are actually very, very mild. What settings are you using for your lights?
Carrara is the most stable 3D app I use and I use quite a few :)
You'll be good to go with any mid-range quad-core, 4gigs of RAM, an entry-level video card, and a decent power supply. $600-$700 will definitely get you into a solid Carrara machine.
On a side note, I've experienced more crashes with C7.11 than C7.0, if that makes any sense.