Which conductivity law should I use to calculate the conductivity of a solution with high/low concentration?
You can use the Debye-Hückel-Onsager limiting law. For a strong electrolyte without the formation of ionic pairs, with $z_+ = |z_-|$, just like $\ce{NaCl}$:
$$ \Lambda_m = \Lambda_m^\infty - (az_+^3 + bz_+^3\Lambda_m^\infty)(c/c^\circ)^{1/2}$$
For aqueous solutions at $25^\circ$C and $1$ atm: $a = 60.6 \, \Omega^{-1}\mathrm{cm}^2\,\mathrm{mol}^{-1}$, $b = 0.230$. For $\ce{NaCl}$, $\Lambda_m^\infty = 126.4 \, \Omega^{-1}\mathrm{cm}^2\,\mathrm{mol}^{-1}$.

References

Ira N. Levine, Physical Chemistry, 6th Ed.