The default configuration isn’t bad as is. I would upgrade to the A10-5800k, to 8gb of RAM (2x4gb sticks), and maybe to the Corsair 430watt power supply (which is 80+ certified, the generic/no names aren’t - will save you money in the long run).
Then just add your choice of Windows 7 Home Premium or Windows 8 Non-Pro (same price). That brings it to $646 and all that is needed is to add a monitor - which can run you anywhere from $75-$125 for the cheapest decent one, depending on resolution (I would go for the cheapest 1920x1080 that is at least 20", personally). Check slickdeals.net and fatwallet.com and search for monitor to see what kind of deals you can get.
Thank you to everyone who responded.
Moving thread from IMHO to Game Room.
My ~7 year old Gateway Phenom died not too long ago so I dipped into our savings and bought a HP Pavilion HPE in that price range. The dedicated video card (GeForce GT 620) is a bit on the low side but works nicely.
I don’t know if you’re still in the looking phase or currently in the gift-wrapping phase but this offer from NewEgg is a very good one (although a hundred bucks more than you were looking to spend).
It’s about a hundred bucks over the cost of the components but that saves you the assembly hassles and gets you the single-source warranty.