I'm a huge Megadeth fan. Countdown to Extinction, Hangar 18, Peace Sells, Killing is My Buissness, and even United Abominations are all great albums.
I'm going to see them with Children of Bodom, In Flames, Job For a Cowboy (I hate them) and some other band on Gigantour! Yay!
BTW, their new guitarist is sick.
Songwise, check out
Symphony of Destruction
Killing is my Buissness
Tornado of Souls
And many more
And if you eventually REALLY REALLY REALLY like Megadeth, go buy the warchest. It's a box with every song ever written by them.
Oh, and Rust in Peace...Polaris (2 differant sounds, both good) Are good too. I think Rust in Peace is an album, too.