There is no proper way to hold a guitar pick. Do what feels best to you and gets the sound you hear in your head. With that in mind, here is some information on how I hold a pick, and the methodology behind my madness
The picks I use are Dunlop Tortex 1.14mm which I chose because they are the stiffest picks for their given thickness. For comparison, they're a lot stiffer than the standard Fender Heavy as well as being less slippery and more durable. I like a very powerful and immediate sound and the stiffness helps with that. The fact that these picks are also less slippery is great for live playing or extended jams when your fingers start to get quite sweaty. I choke up on my pick quite a bit which also enhances the natural hardness of the pick
I move my wrist in such a way that I pick at an angle to the string (see Fig 1). There are two reasons for this. When picking at an angle, there is less resistance across the strings than picking "flat." The natural roundness of the end of the pick allows it to glide back and forth across the strings rather than grabbing at them. My picking angle also allows me to get more flesh into the attack. Fig 1 shows pink highlighted areas indicating the parts of my thumb and fingernail that hit the strings during my playing. Hitting the strings with plastic alone sounds very sterile to my ears. I much prefer the organic tone I get from putting quite a bit of "finger" into it as well. This is especially great in heavier rhythm styles where it can add a lot of extra chunt and aunch to the note. I turn my hand a bit more during lead playing which causes my thumb to connect with the strings more toward its tip, facilitating easier and quicker pinch harmonics. My picking angle causes my picks to wear unevenly at the tip. The shaded areas in Fig 2 show the wear pattern on one side of the top and bottom of the pick.
When I'm playing lead I roll my fingers a bit which causes a little more of the pick to stick out. This helps create a cleaner attack on the strings for better note definition. Look at Fig 3 and notice how much more of the pick is showing at the tip while I'm playing lead.
Fig 1 Pick angle and points of contact
Fig 2 The pick wears unevenly at the tip
Fig 3 Change of pick attack for different styles