When one sweep picks, keep in mind that the slower one practices, the cleaner of a player one becomes. My theory is that no matter what technique of Guitar playing you use, or try to learn, no matter if self taught or not, one will eventually learn the specific technique. For example, I used to practice Guitar playing for ten hours a day, every day when I was in High School. Therefore, continue practicing your sweep picking with the techniques you are using until you feel confortable enough to coordinate your left and right hand. I do not believe in starting out with only three or two string sweeps. I started with four to six string sweeps playing "Judas Priest" types of sweeps. After you've done this, choose an Arpeggio, and follow my advice:

Although Pick-Ups make a difference in tone and sound, a well practiced Guitar player can make any sweep, on any Guitar/Pick-Up sound clean, and well no matter if playing on active or passive Pick-Ups.
Palm muting is your best friend; Learn to palm mute with both hands. Mute the notes you have pluck with your pick on your left hand using your free fingers only after picking them, and palm mute the lower octave notes with your palm on your right hand, and vise versa for left handed Guitar players.
Simultaneous muting with one's hands will result in professional sounding sweeps. Take into consideration though, that it will take extreme measures in practice for one to feel fluent in sweep techniques, but this is an advanced sweep technique that uses both hands to mute.
Tilt your pick slightly so that the pick hits the strings away from the tip. This allows for smoother down strokes and/or up strokes.
One thing I take for granted, but no one else should is metronomes. Use them, they will make your sweeping much more attained and sounded with feeling and expression.

Let me know if you have more questions on sweeping or other Guitar techniques.

-Ron