Here's what I did with your budget:
Desktop:
AMD A10-5800K Trinity 129.99
MSI FM2-A75MA-E35 Micro ATX MoBo 59.79
G.Skill Ripjaws series 8BG DDR3 1066 MHz RAM 79.99
Refurbished: Western Digital WD5000AAKX-FR 7200 RPM 500GB HDD 89.99 (45.00 instant savings)
Diablotek CPA-8821 ATX Mid Tower 45.99 (21.00 Instant Savings)
SeaSonic SS-350ET Bronze certified 350W ATX12V PSU 44.99 (5.00 Instant Savings)
Total cost w/o shipping: 379.74 (if you wanted a good video card I'd plan on spending around $100-120, however the processor I chose has a built-in GPU)
Notice I skipped on the DVD drive and was only able to build a tower, there are no peripherals (keyboard, mouse, speakers, monitor, etc.), so hope you weren't looking for those too. I had to be skimpy on some parts and even then barely came in under $400 not counting shipping or the optional graphics card. $500 can build you a mid-grade tower and it might be able to do all that you want semi-smoothly but I wouldn't count on it running spectacular while recording and playing.
To sum things up, you'd be better off saving that $400-500 until it becomes $800-1,000, then you could build a really top-notch computer and not have to worry about losing any amount of performance. You might even be able to afford your input and output devices (keyboard speakers mouse monitor).