The characteristic murmur of mitral valve insufficiency is best identified by:

The characteristic murmur of mitral valve insufficiency is a systolic murmur that is best heard at the apex of the heart and often radiates to the left axilla. This is due to the backward flow of blood from the left ventricle into the left atrium during ventricular contraction, which creates a turbulent blood flow that produces the murmur. The timing of this murmur coincides with systole, reinforcing the association between the valve dysfunction and the systolic phase of the cardiac cycle.

In contrast, other options describe different types of murmurs that are associated with distinct cardiac conditions. Diastolic murmurs are typically related to conditions such as aortic regurgitation or mitral stenosis, and they would not be characterized as systolic with radiation. The mention of a "snap" refers more to the murmur associated with mitral stenosis due to the opening of the stenotic mitral valve, which occurs in diastole. Moreover, a generalized diastolic murmur is not characteristic of mitral valve insufficiency.

Thus, the specific features of the murmur associated with mitral valve insufficiency—its timing, location, and radiation—clearly align with the correct choice.