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Sorry I missed a couple of the clues.

So, your budget is pretty substantial. You should be able to do a lot with it. Your tech skillz & desire to spend time building & configuring are now one trade-off against available funds.
The OS question relates to cost and performance. Cost not an issue as you have Win 7 license. If you know linux, you can setup a pretty lean server on lower end hardware, saving some $$s. I'm still too n00b @linux right now to offer serious support that way, just pointing it out. There are at least a dozen fairly main-stream distros that'll take care of your needs.
I'll go with the other recommendations here as far as low-cost server box. I'd think you can get far more power than you can possibly need for ~$400 or so. Your needs are pretty slim, so a 2x core AMD of some sort and 4GB RAM should do you fine, which you can build from a PC kit.
I use newegg as a place to start, and rarely can beat their deals. So, that's where I pull examples from when I'm going fast; it's by no means my recommendation not to look around & see if you can do better.
Something like this could do you, and a very comfortable margin more powerful than you need:
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http://www.newegg.com/Product/ComboBundleDetails.aspx?ItemList=Combo.472937Mobo is excellent, processor is overpowered, case would accommodate at least six drives, PSU is a bit lean for four or six drives, though; might be looking at upgrading that into the ~600W range.
You could put 4 drives in this and then get a 4-drive NAS that connects by USB 3 or eSATA or get a Gbit NIC
This build combo:
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http://www.newegg.com/Product/ComboBundleDetails.aspx?ItemList=Combo.472963is very similar. Processor is 2x core, but hyperthreaded to simulate 4. 700W power supply is more interesting. Mobo less exciting, you lose the USB 3 & eSATA options & get fewer expansion slots to play with.
Compare those to something prebuilt:
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http://www.newegg.com/Product/Product.aspx?Item=N82E16859105777Anyway, you're under $500 & you've got the base system built. The AMD option is powerful enough to install linux & run a virtualization or two of WinXP or Win7 if you wish. Also, it's more PC=like with graphics & whatnot, so you can access & manage it more like logging into a remote PC than getting stuck at a command line or crippled GUI. Maybe that offers some flexibility you can use.
Now you're looking at drives.
Unfortunately, since this morning newegg has finished with their promotion of Western Digital 2TB Caviar Black drives. They were $150 each, so you could of had four (8TB) for $600. For a couple more days you can still get them for $180 using a promo code:
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http://www.newegg.com/Product/Product.aspx?Item=N82E16822136456Normally I'd steer clear of 2TB drives, but I'd be willing to place a bet on the Caviar Black series. Of course there are many other options, as some have been mentioned. The Eco & Green drives by several manufacturers give me a Not So Good feeling ... Seen a lot of hard luck stories with those over the past 4 - 6 months.
A possibility here is get one performance drive to run the OS on, possibly even grabbing a 60GB or 64GB SSD and then RAID four 1.5TB or 2TB drives. Even with a board that has SATA 6GB/s native, you really only need the 3 GB/s drives for what you want.
Figure you'll probably find another ~$150 in misc support hardware (like a couple of ultra-silent fans, a Gbit router, 100' of CAT 6 cable), you could be in for an 8TB solution @~$1400, or even a good bit under if you go with 1.5TB or even 1TB drives to begin.
Get all that running properly and you could then add a NAS solution direct to the server over RJ45, eSATA 6 or USB 3 a month or four down the line for ~$600-$800 and you'll be right near your budget limit and be rolling with 12TB (minimum) or maybe up to 16TB.
Actually, though, don't forget you'll want substantial surge protection & UPS to protect everything, so you'll probably be looking $100 up to $200 for one of those depending on power & features.
And, of course, upthread are several suggestion where costs could be trimmed. You might be able to come in the ~$1500-$1600 range when it's all done.