It depends on a number of factors, but in general: no, RAM faster than 1600MHz doesn't give you much of a boost. If the price was the same and you were interested in RAM overclocking, sure grab a 2400MHz kit, but otherwise 1600MHz will likely be just as good.
Some of the factors are:
- What tasks are you running (rendering? gaming? office stuff?);
- If gaming, is the game CPU-bound or GPU-bound (the former may benefit from faster RAM, but even then most don't);
- Are you using onboard graphics or a dedicated GPU? Intel onboard doesn't seem to scale like AMD APUs with RAM speeds, but may make a difference.
A couple of articles using the 3770K that show 1600 more or less the same as 2400 except in some specialised cases:
On expansion: Try and run in dual-channel. If using existing RAM, try and match the specs as closely as possible with any new RAM you buy. Keep the paired sticks running in corresponding dual-channel slots. While DDR3 incompatibility seems relatively rare, there is no guarantee separately purchased sticks will work together -- you'd need a manufacturer-tested 4x8GB kit to get that guarantee.
When looking for RAM compatibility, Intel's list is pretty limited. RAM suppliers often have their own lists. (As an example, the listing for G-Skill Ares has your motherboard in the QVL).
