  Given an odd prime number $p$ and a $p$-stabilized Artin representation
$\rho$ over $\mathbb{Q}$, we introduce a family of $p$-adic Stark regulators
and we formulate an Iwasawa-Greenberg main conjecture and a $p$-adic Stark
conjecture which can be seen as an explicit strengthening of conjectures by
Perrin-Riou and Benois in the context of Artin motives. We show that these
conjectures imply the $p$-part of the Tamagawa number conjecture for Artin
motives at $s=0$ and we obtain unconditional results on the torsionness of
Selmer groups. We also relate our new conjectures with various main conjectures
and variants of $p$-adic Stark conjectures that appear in the literature. In
the case of monomial representations, we prove that our conjectures are
essentially equivalent to some newly introduced Iwasawa-theoretic conjectures
for Rubin-Stark elements. We derive from this a $p$-adic Beilinson-Stark
formula for finite-order characters of an imaginary quadratic field in which
$p$ is inert.
  Along the way, we prove that the Gross-Kuz'min conjecture unconditionally
holds for abelian extensions of imaginary quadratic fields.
