I need RAM upgrade path/Please need EXPERTS.

Ok currently Im running two dif mem chips 1 2gb and 1 4gb (which I hear is not good). Both are DDr3 and Im almost positive both are 1333Mhz. So Im looking to upgrade ram to be able to get better game performance, my gpu (which I know is outdated n not that good) can handle the games I play beyong the standard of whats needed. My only problem is the graphic SPEED, like if I play a online MMORPG like WOW or Neverwinter... it sets my graphics almost at high but rendering speed is all the way at low.. so Im guessing this is ram! ... What would you guys suggest (within a 25-75$ budget) I do to my ram to upgrade and get better performance? I was also told APU's (which I have the AMD A8 5600k) run off system memory. I hear my APU is better than my GPU which is a (Geforce GT 520) but when I switch to the APU it lags my system because the ram sucks. So I would like to have enough mem power/speed to run the APU for games. .

CPU- AMD A8 5600k
GPU- Geforce GT 520
MEM- 6GB (DDR3)
MOBO- BISTAR A55ML2
OS- Win 7 64bit

***CPUz MEMORY REPORT***


DIMM # 1
SMBus address 0x50
Memory type DDR3
Module format UDIMM
Manufacturer (ID) Micron Technology (2C00000000000000)
Size 2048 MBytes
Max bandwidth PC3-10700 (667 MHz)
Part number 16JTF25664AY-1G4D1
Serial number DB3BD9CD
Manufacturing date Week 20/Year 09
Number of banks 8
Nominal Voltage 1.50 Volts
EPP no
XMP no
AMP no
JEDEC timings table CL-tRCD-tRP-tRAS-tRC @ frequency
JEDEC #1 5.0-5-5-14-19 @ 380 MHz
JEDEC #2 6.0-6-6-17-23 @ 457 MHz
JEDEC #3 7.0-7-7-20-27 @ 533 MHz
JEDEC #4 8.0-8-8-22-30 @ 609 MHz
JEDEC #5 9.0-9-9-25-34 @ 685 MHz
JEDEC #6 10.0-10-10-28-38 @ 761 MHz

DIMM # 2
SMBus address 0x51
Memory type DDR3
Module format UDIMM
Manufacturer (ID) Team Group Inc. (7F7F7F7FEF000000)
Size 4096 MBytes
Max bandwidth PC3-10700 (667 MHz)
Part number Team-Elite-1333
Manufacturing date Week 29/Year 13
Number of banks 8
Nominal Voltage 1.50 Volts
EPP no
XMP no
AMP no
JEDEC timings table CL-tRCD-tRP-tRAS-tRC @ frequency
JEDEC #1 5.0-5-5-14-19 @ 380 MHz
JEDEC #2 6.0-6-6-17-23 @ 457 MHz
JEDEC #3 7.0-7-7-20-27 @ 533 MHz
JEDEC #4 8.0-8-8-22-30 @ 609 MHz
JEDEC #5 9.0-9-9-25-34 @ 685 MHz