I don't suggest that PC, the motherboard, though compatible with AM3+ processors, is not ideal as it doesn't use the AMD 900-series chipset which was designed for FX. That older motherboard is compatible, but lacks some of the features that make FX a good choice. The graphics on the motherboard are also very, very low end.
Let's strip this down to the basics. You said you will be using your own hard drive, RAM (Make sure your RAM is DDR3-1600 or better), and sound card (Not really necessary with on-board audio, but add-in cards are often better for audiophiles or people working with music), and optical drive. You'll certainly save some money reusing components. This means you will need a case, motherboard, CPU, power supply, and operating system. Below are some suggestions for components.
Case: Antec Three Hundred - A simple case. All you really need is a case, either mid-ATX or full ATX, that is compatible with standard ATX motherboards. $54
Motherboard: MSI FM2-A85XA-G65 FM2 AMD A85X - This motherboard is a standard ATX that takes AMD's newer FM2-based APU's. $99
CPU: AMD A10-6800K Richland 4.1GHz - This is one of AMD's flagship APU's. These include the graphics and CPU onto one chip. $139
Power Supply: CORSAIR CXM series CX500M 500W - Should be more than enough power for this PC. $70
OS: Windows 8.1 64-bit OEM - You need this. $99
Grand Total: $464
Other hardware you may need.
RAM: G.SKILL Sniper Series 8GB (2 x 4GB) 240-Pin DDR3 SDRAM DDR3 1866 - In case your current RAM is incompatible. $79
HDD: Seagate SV35 Series ST1000VX000 1TB - Should be enough. If your current drive is older than five years, consider replacing it. $74
ODD: LITE-ON DVD Burner - Bulk Black SATA Model iHAS124-04 - A basic drive is all you need. $17