IMO EQ and effects play the most part.
I use overdrive as my staple sound, with a hint of delay dialled in and chorus during the solos when necessary.
My EQ is something like Bass 10 o'clock, Mids 1 o'clock, Treble 3 o'clock, gain on 1 o'clock, if I'm playing low-gain rock. For heavier music like Metallica I use Bass 1 o'clock, Mids 9 o'clock, Treble max, gain at 4 o'clock.
I still use the traditional right hand approach though, hand on bridge, pick held between thumb and first joint of index, though at one point i was picking with my index finger pointing perpendicular to the strings.