For home office use there is no real advantage either way between AMD or intel. since you are comfortable with AMD I went that router with this build.
the A8 APU' graphics should able to run games fairly well @ 1280x1024 as long as you keep the AA/AF turned down. I put a SSD in the build vice a dedicated GPU, but left the option at the bottom for you to swap. you can drop the price down if you can re-use their old DVD and HDD. I would use the SSD as a boot/apps drive and their old HHD as mass storage (if they are SATA)
I would go without the dedicated GPU to start with, you can always upgrade later. AMD just annouced price reduction on the HD 7770 to compete with the new nVidia products. the HD 7770 would be an ideal medium/light gaming card.
Still debating if they need/would notice having a SSD in the computer. Here is another one I threw together combining some things from both builds with no SSD. All I know I was told is they want it to run fast(not load windows fast, but internet browsing, etc fast and lots of storage). Will be ordering tomorrow night.
LG DVD Burner Black SATA Model GH24NS90
Rosewill R101-P-BK 120mm Fan MicroATX Mid Tower Computer Case
Western Digital Caviar Black WD1002FAEX 1TB 7200 RPM SATA 6.0Gb/s 3.5" Internal Hard Drive -Bare Drive