What decides -1/2 and +1/2 spin values of subatomic particles?
Spin is an intrinsic property of any nucleus, and can be 0, 1/2,1, 3/2, 2........ A nucleus of spin I can adopt 2n+1 stable states or orientations. For 1H, I=1/2, and this means it can adopt two possible stable spin states; +1/2 or -1/2. The energy levels of these two spin states are different (and proportional to the strength of the magnetic field); one is slightly higher than the other, and so there is a population difference between the two states. However, the energy difference is incredibly small, and difference in populations (called the Bolztzmann distribution) is only about one in a million. The individual nuclei can hop back and forth between the two states quite readily, provided there is sufficient energy transfer (into or out of) the system. Indeed, this is the basis of the NMR experiment - we can manipulate spins between the two spin states with relative ease.

For a nucleus with a spin greater than 1/2, there are more than 2 stable spin states that the nucleus can exist in. Deuterium (2H) has I=1, and can adopt one of 3 stable spin states. The distribution of spins amongst these states is approximately equal (less the BD of approx one in a million). Any individual nucleus will switch between these states. Lutetium176 has a spin of 7, and so can adopt 15 different stable spin states.