I'm assuming that budget doesn't include screen or mouse/keyboard.
Office PC
It's Micro-ATX, comes with built in graphics and the case is fairly small. Two 1TB drives in RAID 1 should ensure that you don't lose any data.
Price is around $800. Which leaves a little room to buy a new shiny LCD screen.
This should be suitable
AOC 23.6" screen.
This is a typical recommendation from most sites. Provides a bit of room to upgrade in future and he will think he's playing with a super computer after coming from a P4 system.
