Hand position is very important in the way that you strike the string, what I like to call "setting the string in motion".  The way the string vibrates really determines the sound you get.  The way I explain "setting the string in motion" is to know that the string can move horizontally or vertically or somewhere inbetween.

To get the purest sound of the string that is vibrating over the pickup, you want to move the string as horizontally as you can.  So, in essence, you are trying to move your pick(s) straight through the string by pulling it towards you with your finger(s), or pushing the string away from you with your thumb. The pick should push the string straight (horizontally) and eventually come upward off the string.  That is the motion you are trying to create (horizontal picking).  What you don't want is for the pick to attack the string at an angle (non-horizontally).

The correct postion of your your hand and fingers can set you up to create the correct motion easier. A general rule for the hand postion is for the fingers to be curled like the "letter C" and the thumb sticking out straight down the strings away from the fingers. The fingers should be curled somewhat but the biggest mistake I see in my students, is that the finger tips are too far curled under the middle joint of that finger. Try to keep the finger tips on top of the middle joint, but without going behind it. The more you can keep the finger tips out in front of the finger joint, the easier it will be to move the string horizontally. Also it puts your hand and fingers more in a natural postion with less tension on your joints and then you are able to move the fingers more fluidly and get the sound you so desire.