Recommend refurbished route - example: http://m.tigerdirect.com/products/3393962

I have built several PC's in the last few years using a case at about $40.00 and a PSU (400 W) at about $20.00 which were new items purchased on sale/rebate at Newegg.com. You can easily spend more than $150.00 for a case alone if you are persnickety. It should not be hard to find a new 1 TB HD for $40.00-45.00. Do not even think about getting an SSD on this budget. So long as you do not plan to overclock, stock coolers and standard desktop memory should be fine. My final builds typically came out at about $500.00 but the big cost was the MB and Intel chip, buying the models that were getting rave reviews a couple of years previously at substantial savings is the key. The law of diminishing returns applies bigly in computer performance, and a surprising number of top performing machines never get used in a way that shows the marginal performance benefits extra thousands will yield. The best way to buy your parts is to wait until what you need shows up at prices you can afford, and of course you will be spending a lot of time shopping that could be spent better doing almost anything else. A part time job to earn the money to buy a good pre-built might make more sense. 

Thanks for the replies everyone.  they were all very helpful.  I will let you know what I did.  

I built a new system a while back with this case, power supply, and drives = $142.79, not counting CPU, RAM, mobo, and SSD.  That leaves $207.21 in your budget for the rest.  Find a good microATX board, CPU, and RAM for that and you're all set for $350.00 total
 
Rosewill Dual Fans MicroATX Mini Tower Computer Case FBM-01  $24.35
https://www.amazon.com/gp/product/B005LIDU5S/ref=oh_aui_detailpage_o07_s00?ie=UTF8&psc=1
 
Corsair CX Series, CX430, 430 Watt (430W) Power Supply, 80+ Bronze Certified  $50.66
https://www.amazon.com/gp..._s01?ie=UTF8&psc=1
 
Lite-On Super AllWrite 24X SATA DVD+/-RW Dual Layer Drive - Bulk - IHAS124-04 (Black)  $17.79
https://www.amazon.com/gp/product/B002YIG9AQ/ref=oh_aui_detailpage_o07_s01?ie=UTF8&psc=1
 
WD Blue 1TB SATA 6 Gb/s 7200 RPM 64MB Cache 3.5 Inch Desktop Hard Drive (WD10EZEX)  $49.99
https://www.amazon.com/gp...es01?ie=UTF8&psc=1

You mention using it for Tracking only.  The requirements for tracking are much less than mixing/mastering.
When I track remotely, I do it with an old version of Sonar (8.5) on a dual core laptop and external USB hard drive (7200 RPM is a must!).
 
Then I save the project and bring it into my Sonar Platinum rig at home (which is underpowered according to most people!).  Note that My tracking is AUDIO only and I do not do much MIDI even on my SPLAT rig.
 
If your interface supports it, an older refurbished machine may work for you.