Yes 1600 is better. Here is a link to corsair 1600 8gb $45 w/ promo code http://www.newegg.com/Product/Product.aspx?Item=N82E16820233144
You could add a hd 7770 for low-med gaming or hd 6870 med-high gaming. You would have to get a 500w psu to use the 6870.
The 1600 mhz is not better for the build. An i3 2120 is designed for 1333 mhz RAM, so if you put in a 1600 mhz RAM it will automatically reduce to 1333 speed in bios unless you OC it. There is little noticeable difference to the user.
If 1333 mhz is cheaper, just go with it. Spending more for 1600 mhz will have no gains.
Should natantantanta chooses to upgrade to an Ivy Bridge CPU in the future, 1600 mhz RAM will be more appropriate.
For regular non-gaming use, 4 GB is more than enough. If using photo-editing/video editing programs, then 8 GB would be more useful.