Origin of different brainwaves
Alpha and beta brainwaves are just two of several arbitrary, named frequency ranges for a brain-wide phenomenon. See Types of Brain waves. These so-called brainwaves are big electrical events that sweep across the entire brain.

My recommendation for electrode placement is based on my engineering experience. Pick any location on the scalp. You could start with the temples. Take your measurements. Then move the electrodes to a different location and repeat the measurement. Continue this experimentation until you discover by observation which location yields the best results. When you have finished with the experiment, you can post your experimental results on SE Biology and answer your own question.

I suspect that electrode type and method of contact (dry versus conductive gel) will be more significant than actual placement on the head.