Well, part of learning to use a plectrum is to find one that fits what you're playing. Electric guitarists tend toward thin picks, and mandolin players toward stiff ones (I do, anyway) because you're dealing with double-coursed strings with a reasonable stiffness to them.

Acoustic guitarists tend toward the medium pick, but then again, some likes 'em thick and some thin. If you're strumming a lot, thinner picks slide over the multiple strings better than the stiff ones. Single-note playing requires stiffer picks, I think.

I use Fender mediums or the equivalent for guitar, and tortoise-shell for mandolin. For electric guitar, I stick to the mediums, though thins sometimes seem "right." For tenor banjo, I use the mediums, again.

By the way, since tortoise picks are illegal to sell, so people try various substitutes. I recently tried, and like, buffalo horn picks that I got on eBay -- they were mailed from Ho Chi Minh City! Nice picks, though.

Now, how to hold the pick. This is the bigger problem, to my mind. I usually tell students (when I have 'em) to make a "trigger finger" with the index finger, folding the finger like one would with a trigger. Place the pick on top of it. Place the thumb on top of the string, so that the part of the pick you want to use (the point or the round part, whatever) and strum/pick with your palm parallel to the strings. I have seen people hold the pick out at the end of the finger and thumb, sort of like pinching it, and I think that posture leads to more pick movement than you want (and sort of wimpy tone, too).

I have no preference or good advice on the size and shape of the pick, since that's a matter of taste. Try a lot of them, and see what works for you. Several years ago, I even saw someone making and selling stone picks. I never figured out how to make those work, I can tell you.

Good luck.

Bob