Should I sample at twice the bandwidth or twice the highest frequency?
Well, according to Nyquist-Shannon theorem you should sample at a rate which is at least twice the highest frequency you want to capture. This is also referred to as the sampling theorem because it "forms the basis" for sampling.

Now regarding your specific question, I have to say that cos(4*pi) (along with the rest of the components) is just a number which is equivalent to a DC signal. In case you imply cos(2 * pi * 4 * n/fs) (the same for the rest of the components), where n is the sample index (constantly increasing) and fs is the sampling frequency, you should sample at twice the highest frequency (which in this case is 4), which is 8.

As you might be able to say, this would produce a result (just for the first component, but similar for the rest) cos(n * pi), which has a period of 2..., which in turn means that you would get precisely two samples per period. Now in the case you happen to sample at the zero cross, all samples would end up being zero (just for this highest frequency).

I strongly suggest you have a look at some academic literature regarding sampling. I would suggest Proakis' &amp; Manolakis' Digital Signal Processing - Principles, Algorithms and Applications and Orfanidis' Introduction to Signal Processing