Gaming upgrade with a $600 budget?

No SSD, no burners, just a rig with a 2TB Seagate Barracuda HDD

1 x Intel Core i5-4460 (3.2GHz, 6MB, LGA1150) box
$433

1 x Asrock Intel 1150 Socket B85M Pro3 M-ATX MB
$153

1 x Zalman Z3, USB3.0 black, 3x120mm
$110

1 x HDD SEAGATE Barracuda (3.5",2TB,64MB,SATA III)
$209

1 x Fortron Raider S PSU 650W, 80+ SILVER
$200

1 x Sapphire R9 390 NITRO, Tri-X OC, 8GB GDDR5
$962

=$2067

With those upgrades I mentioned (including that 1TB drive), you could also pair them with more RAM

1 x Intel Core i5-4460 (3.2GHz, 6MB, LGA1150) box
1 x Zalman Z3, USB3.0 black, 3x120mm
1 x Seagate Barracuda HDD (3.5", 1TB, 64MB, SATA III)
1 x Sapphire R9 390 NITRO, Tri-X OC, 8GB GDDR5
1 x Asrock H81M-HDS (S1150, USB3.0 Header) mATX
1 x XFX TS Series 550W, 80+ Bronze
1 x Kingston DDR3 1600MHz, C11, 8GB

Total: $2178

You could potentially combine these $11 with another drive, but this setup offers the best bang for your buck. Personally, I wouldn't touch anything else beyond this.