In random order , with last question first :
.38 +P in the better loadings , is reasonably adaquate .
From your profile ; if New Jersey ( affirmatively) Legal is a relevant parameter , your best choices are Cor Bob PowerBall and Federal Guard Dog , formerly EFMJ .
Back in the Late Revolver Era , R-P made a " Medium Velocity " 125 JHP for exactly that purpose . Various regional loaders did/ still so , mfg similar.
Considered as a class , .38 Spl +P+ " Treasury Load " , various boutique +P , plus the Original .357 Mag 110 JHP , still seen 8n WWB , plus various Boutique +P , will meet your power and controlability criteria . As a class , they will be closer to 10 inch of penetration than the Theoretical holy grail of 12 to 18 inches . Your decision how much you subscribe to Theoretical Holy Grail vs Real World results will shape your preferences .