I’m new to umpiring and have become quite fascinated about the psychology of the different guards’ batters choose when they come out to bat.
Batters ask for middle stump, leg stump, middle to leg, one leg, leg stump to off stump and other variations. Can I ask what you choose and the reason why?

Batters take a guard to know where the stumps are and to make them feel in control

I always batted on centre with my feet level until I was around 20 then I was bowled around my legs sweeping twice in a match by former Qld spinner John Hill.

Our coach John Bell suggested I take 2 legs which I continued for the rest of my career

I remember my father telling me the importance of knowing where the stumps are and making the bowlers bowl to you.
As a left hander he suggested taking one leg as a guard and I’ve done so ever since.

As mentioned by others, it is to enable the batter to be aware of where his stumps are, and being able to cover them with their footwork. I played through junior cricket on centre, and then continued using centre as my reference point through my grade cricket career and still do now, playing Veterans cricket.
What I do now is vary where I stand in relation to centre, based on the wicket conditions and bowling. I move deeper in the crease, out of the crease, leg stump, off stump, sometimes multiple times per over in an attempt put pressure on the bowler. It helps when considering their field placements and my intent to increase the chance of scoring runs.

I always asked for middle. I felt I could adjust slightly to off or leg depending on the bowling and the wicket. I guess it’s also what you get used to.

I’ve changed over the years. To me it’s just knowing where I am in relation to off stump. I’m a lefty and I bat on leg now, so knowing where I start allows me better knowledge where I end up if I move around the crease in order to score

Always leg stump

Great question... for me... and agree with the concept of knowing where your stumps are... It's all about the head position in relation to the stumps.

As a generalisation... right-handed batters look to have their right eye on the off stump. Anything outside the line of the eyes is missing the stumps then. We can't see behind ourselves. So lining up our eyes to stumps helps us to know where the stumps are behind us.

Now... how to get your eyes there consistently.

Crouched stances will naturally have the head more towards the off side. And upright stances will do the opposite. SO players with crouched stances could technically have their feet on the leg stump and their head on the off stump. Viv Richards a good example of this. Players who are more upright might be more towards middle stump and at times middle and off or even off stump.

When players trigger all of this I just explained goes out the window and it becomes more about where the player finishes after their trigger. ie Head on off stump.