Whenever I think of the Krieg regiments, I think of Churchill's quote: "A fanatic is one who can't change his mind and who can't change the subject."
The Krieg regiments are kind of the 40k logical conclusion of what the Imperial Guard should be - effective, fearless, content to be mown down in their millions on horrific battlefields. As such, they're a world away from the "Abnett" style Imperial Guard, who are very human, for better or worse.
I thik the best way to play them is to explore forcing them to let their underlying humanity gradually peek through over a number of sessions.
At first they should be dour, fatalistic, religious fanatics, but exposure to elements beyond their experience - other modes of thought, philosophies, happiness, love etc - could cause them to question their underlying beliefs, forcing them to make moral choices unfamiliar to them. This gives an intelligent player an opportunity to let his character have a proper "arc," gradually growing into something more than he originally was.
Of course, a perfectly legitimate alternative is for the player to refuse to grow, refuse to have an arc…to react badly to these choices, and respond with anger, blind hatred, reactionary religious fanaticism etc. Either approach works. Indeed,the second is arguably more in character for a Kriegan.