How could one can say that frequency spectrum having Nyquist frequency 'x' is the most appropriate representation of a given signal?
The most important thing is to sample at more than twice your signal's bandwidth; the period is largely irrelevant. Say your signal with period 2 is a square wave -- its bandwidth is infinite and you'll never be able to sample it correctly (at least in theory). If your signal is a sine wave, then a period of 2 means its bandwidth is 0.5 and you'll easily sample it adequately.

Personally, whenever possible, I'd sample:


a bit above Nyquist (say, at $2.2B$, where $B$ is the signal bandwidth), to maximize the number of useful frequency bins, and
for as long as possible, to increase the spectral resolution.