^It depends on the MOBO and CPU, and yes some CPUs will not benefit or use the faster RAM, and yes faster frequency RAM can be run at lower speeds. Oddly for example, the SB CPUs seem to in some cases actually perform worst with the 1866 or 2133 MHz speeds, and there's almost zero gain with >1333 MHz frequencies, so spending 400% more on some RAM is crazy. Conversely, X58 seems to perform better with higher frequencies less than 2200 MHz with low & tight CAS with 2~8 FPS gains; in the X58 1600 MHz CAS 8-8-8 is the better choice. AMD seems to share the X58's affinity towards higher frequencies to a point and only the 6-cores benefit or in many cases use RAM >1600 MHz.
In the OP's situation find the best 1333 MHz with the lowest 'tight' CAS {tight 8-8-8 or 7-7-7 vs loose 7-8-7}; otherwise get more RAM with a higher CAS, but don't exceed CAS 9 1333 MHz. Clearly, the Athlon II X4 645 can run 1600 MHz RAM.
However, if I had to choose between spending >$50 then it would go towards a better GPU {improved FPS} or SSD {overall performance}.