Color management help
Ian Lyons has "always" had the most comprehensive tutorials on Photoshop Color-Management: with step-by step screen shots.
Should tell you everything you need to know---- And, no, a monitor should not be set to Adobe RGB--- Adobe RGB is a "work" space within Photoshop, & uses the monitor profile established in the Color/Profile.
Weather you use the monitor's generic profile, or youse a profiling devise can make a difference in the final output.
|Bald Eagle by anisah|
from Features - lips/mouth
|heron and fish by APenza|
from A Big Year - birds
|Cows Cowering Under Rare California Super Cell by RBFresno|
from -The Old Cows-