Grab a i5 3570K (updated version of 2500K at same price)
4GB RAM, or if you have any money left over get 8GB. But not that most games do not make use of a system with more than 4.
AMD HD 7770 would be OK. But you can easily opt for a more powerful graphics card if budget allows, like the 7870.
Not sure what you can get with $600. Here in the UK prices on hardware are expensive, especially with tax/VAT added on...
Only grab a SSD as last priority. It does not help with FPS, so if your gaming it would be better spent on a CPU or graphics card.
Edit: Just noticed you did not want to build it
I would recommend having a look at some Newegg videos on how to build a computer on YouTube. It's soooo easy to do and you can get more for your money that way.