Job for a cowboy's " Entities " song has a solo with sweep picking at the end, it's the first sweep picking I ever learned, it's really easy. Just look up the tabs on ultimate-guitar.com
As far as tips go, don't pick every string out, start slowly but make sure your motion is fluid, and goes all the way through. I wouldn't reccomend muting the strings as you learn, as it's a bad habbit to get into.
Try doing :
----------13^17h^13
-----15------------------15
14---------------------------14
It's a simple fraction of the E Minor Arpeggio and was one of the first I learned. It's fun and easy to play and practice with. That solo I mentioned above uses E Minor a lot, it's one of the easier ones to play and is very popular in DeathMetal/DeathCore bands, as is A Minor, but I wouldn't reccomend starting with that one
If you get bored of that one, or A Minor ( You can find tabs for them on the net easily ) I'll show you Diminished and a few others. Diminished is probably the most popular Death Metal scale of all time, and is in tons of famous DM songs/solos, like The Exorcist solo from Possessed, the solo from Infecting the Crypts by Suffocation, and too many others to name.