I've been through that phase of relentlessly practicing monotonous alternate picking staccato exercises. At the lower frets (1-7), I think it is better to keep your fingers perpendicular to the fretboard since the frets on this part are far apart from each other. It is also easier to play clean legato with the fingers perpendicular to the fret-board. But as you go to the higher frets, it is easier( for me) when the fingers are slanted toward the body. To do this the thumb would naturally curl around the neck for a better grip.