Importance of Newton's First Law of Motion

The first law is never used directly to solve a numerical problem, yet it is indispensable conceptually, contributing three distinct ideas.

1. It shows an EQUIVALENCE between the 'state of rest' and the 'state of uniform motion along a straight line' -- both require a net unbalanced force to change them, so both are properly described together as a single 'state of motion'. Whether a given body is described as being at rest or as moving uniformly depends purely on the choice of reference frame, not on any physical difference in the body itself.
2. It DEFINES FORCE conceptually, as whatever entity is capable of changing a body's state of motion. The first law only tells us qualitatively that force is the thing that initiates or alters motion; it is the second law that turns this into a precise, quantitative, mathematical expression ($\vec{F}=\frac{d\vec{p}}{dt}$). …