As the highest note in this tune is the F on the first string you will not have to concern yourself with left hand positioning.
In fact by keeping your left hand at a right angle to the fretboard you should not have any lateral movement in your left hand at all.
Make sure to play the tune at a speed that allows you to include ornamentation. The half moon markings over certain notes in the sheet music are suggested points in the tune at which you can add your ornaments but feel free to place them somewhere else if you so desire. The main point is to include some ornamentation.
For the accompaniment, Tony has included only two chords in this tune; D Minor and C. Sometimes simplicity works best. An uncomplicated accompaniment can be enough for such an expressive tune.