http://pcpartpicker.com/p/1pWhM
Total before tax/shipping, incl. current promos: $1386
That's my recommended build. Your budget is quite generous and allows for a lot of luxuries that will make your PS2 experience pretty much flawless. Some reasons why I picked the parts that are in there:
PS2 adores strong single-threaded performance, and benefits from having four strong threads. The i5 4670K will also allow you to overclock it somewhat (probably to around the 4.2 GHz level) comfortably and get some additional value out of the chip. The Asus board is there mostly to support this overclocking effort (which is something I think you should definitely pursue).
It DOES support SLI, but by the time the GTX 770 starts feeling like you need to upgrade it, the price of buying another 770 will not justify the performance uptick over buying an 970 (or whatever NVidia has out at that point). You should only count on having two cards SLI'd on two conditions (both of which need to be satisfied):
1. You will be playing at a resolution above 1920x1080 (multi-monitor or a 4K TV or something).
2. You will be doing this upgrade within the next 9 months.
If for the next 12 months or longer you're sticking with the monitor you have now, the single 770 will drive any game you need and more. You might even save ~$30 by stepping away from the SLI capability.
PS2 also adores fast memory but only uses around 2 GB of it. This is why you see 8GB of -2133 instead of 16 GB of -1600 or -1866. Fast memory is doubly important if you overclock.
An SSD is a required feature for any machine costing over $1000 in my opinion. Depending on your storage needs, you might also simply ditch the 3TB platter and save another $100.
I recommend a 750 W PSU if you intend on sticking with SLI capability, or if you think you might swap to a Broadwell i7 come next year. Otherwise, you could step down to a 650-700 unit and save $20 or so. I do recommend sticking to the 80PLUS Bronze and above, though - these PSUs put out a considerably smaller amount of heat, and that makes them MUCH quieter, on top of being friendlier to your electricity bill.
The CPU cooler is somewhat arbitrary, but the 212 Evo is one of the most tried and trusted sinks out there, it will keep things both cool and quiet even when you overclock. The case is completely arbitrary and you can pick any one you like.
Last but not least, the OS:
Win 7 Pro is in there per your request, but unless you specifically have a need for its advanced networking and virtualization capabilities, that's $30 out the window. If you're a college student, check with your book store to see if they sell the OS with a student discount - when I was an undergrad, I bought my copy of Win 7 when it first came out for $50.
I'm sure Rbstr will find plenty of nitpicky stuff with my specific part choices, but the headline CPU, GPU and Mobo is what we will probably all recommend.