No game I know of can use more than 2-3gb of ram. A 8gb kit is sufficient.
Considering that ram is so cheap, I would have no problem with a 16gb kit of 2 x 8gb.
You want documented ram compatibility. If you should ever have a problem, you want supported ram.
Otherwise, you risk a finger pointing battle between the ram and motherboard support sites, claiming "not my problem".
One place to check is your motherboards web site.
Look for the ram QVL list. It lists all of the ram kits that have been tested with that particular motherboard.
Sometimes the QVL list is not updated after the motherboard is released.
For more current info, go to a ram vendor's web site and access their ram selection configurator.
Enter your motherboard, and you will get a list of compatible ram kits.
While today's motherboards are more tolerant of different ram, it makes sense to buy ram that is known to work and is supported.
Tall heat spreaders are not necessary with 1.5v ram, and can interfere with many cpu coolers. Look for a low profile kit.
Lastly, the extra $100 or so paid for a 3770K over a 3570K is largely wasted. Few games use more than 2-3 cores, making the extra hyperthreads largely irrelevant.
Spend the $100 on a better graphics card.