The most important thing to keep in mind while practicing sweeping (as with other techniques) is not to be in a rush to play fast , speed comes by time.
You seem like a Metallica fan (like me ;) ) , so I'll tell you where you can find easy sweeps in their songs to begin practicing.
1- Lepper Messiah Solo ... The begining of the solo is just 3-string sweeing throughout ... You should master this one as a first step, cuz you'll find these min/maj 3-string sweep a lot in other songs.
2-Creeping Death Solo ... There's a minor 3-string sweep there , in the middle of the solo as I can remember.
3-Fade to Black intro solo ... Some people play this one with alternate picking ... Anyway I prefere sweeping'em ... You should try sweeping too , at least for practicing... (what doesn't kill you makes you stronger).
4-The Call of Ktulu Solo ... There's a realy cool 4-string sweep in the middle of that solo , it's hard but worth practicing.
You should try some Malmsteen too ... You'll find the 3-string dim sweep in all of his songs !
Marty Friedman makes realy cool & complicated sweeps , Megadeth's "Rust In eace" should be your next step.
And for sure we can't forget the King of sweeps , Jason Becker.