Nothing can take away the importance and brilliance of Master of Puppets, Ride the Lightning and Rust In Peace, they are indeed Hallmark albums and a must have for even the casual metal head.
So far the recommendations have been spot on. I for one couldnt stand growling or screaming for a very long time, but I slowly got into it. The aggression, power, anger, and energy is what makes me listen to metal. The sheer force of a metal band in good sync with one another and chugging along is such a good release.
Safer bets have already been mentioned like Megadeth and Metallica.
Pantera is probably a gradual transition into a bit more screaming and yelling. Still mainstream sounding, not progressive or technical, but some kick ass riffs and chops.
Lamb of God is also fairly easy to get into, if you can stand their lousy guitar solos. Some good riffing, and the drummer Chris Adler is fantastic.
Kings X is not exactly metal, but Dogman is a great album, and probably classified as metal.
These are generally more rock oriented metal that have mainstream appeal. If you get into the various subgenres of metal then you would have to pick favourites from each one based on which subgenres you prefer. I would also suggest giving Pandora a shot, try put in a song you like and see where it takes you from there.