Do I need 1866/2133MHz RAM for an APU build?

I'm planning on building a budget PC with AMD's A10 6800K APU. How much would 1600MHz RAM bottleneck my system? Higher speed memory is pretty expensive. Couldn't I just overclock it instead and save some money? 

To overclock RAM that means you have to have RAM that is overclockable which is just as expensive as already overclocked ram. That 60 dollar pair of 1600 MHz econo ram isn't going to overclock well. My opinion is to get 2x4GB DDR3 2133 MHz ram. It's cheaper than you think and your APU system will love you for it.

I know they natively support (richland) up to 2133 mhz

If you are using intergrated graphics then it will bottleneck you, if you are using a seperate video card then it wont.

APUs by design us normal system Memory (dd3) GPUs by nature love fast drr5 memory. So what can you do about it? BUY FAST RAM. The apu will love the really fast ram you give your system because it's close to the gddr5 gpus are used to. For an APU i'd recomend 1866+ 2133/2400 is optimal.

A10-6800k's have been seen in the wild running with 2400 MHz RAM at 5 GHz CPU speed and just over 1GHz iGPU speed.