If you're trying to stick close(ish) to you budget I ran up something pretty similar to what I have for you.
$625 including the OS (and before any kind of bundle pricing... double check Micro Center for some of this stuff if you have one nearby)
CPU: AMD A10-5800K 3.8GHz Quad-Core Processor$109.99
Motherboard: MSI FM2-A75MA-P33 Micro ATX FM2 Motherboard$54.98
Memory: G.Skill Sniper Series 8GB (2 x 4GB) DDR3-1866 Memory$73.98
Storage: Sandisk Ultra Plus 64GB 2.5" Solid State Disk$64.99&Seagate Barracuda 2TB 3.5" 7200RPM Internal Hard Drive$89.98
Case: Silverstone ML03B HTPC Case$59.99
Power Supply: Corsair Builder 430W 80 PLUS Bronze Certified ATX12V Power Supply$49.99
Optical Drive: Asus BW-12B1ST/BLK/G/AS Blu-Ray/DVD/CD Writer$78.99
Just a few notes/opinions... The AMD APU's are a pretty fantastic bang for your buck these days. I've done two very similar builds using an A10 and an A6 and both performed without a hitch with uncompressed MKV rips using XBMC. (And certainly no need to overclock.)
I picked a case that is reasonably easy to work in and has a great 'component style' form factor but will not allow the quantity of drives you're talking about. My suggestion would be to separate those into an independent NAS down the road
60GB for a boot drive is plenty! I'm only about half full with my Win8 install and a handfull of applications. My games and whatnot go on the secondary HDD.
For reference I've got almost the exact build listed here and it works really well for the kinds of things you're asking for. I've even used mine for some light gaming and it's handled things better than I'd expect (like playing Arkham City at 40+ fps on medium settings). That being said if I'm looking to play the latest games at 60+ fps on ultra settings I go into my office and use my desktop outfitted withan OCed i7 3770k coupled with 16GB or RAM and a GTX770.