It's totally up to you man.
Myself, I tend to be a picker most of the time...but it's just how I learned...it's not the "Right" way or anything. Listen to different players and see what sorta sound appeals to you the most. Guys like Steve Morse, Vinnie Moore, Al Di Meola, Zakk Wylde, etc., tend to pick most all of their notes. Dudes like Allan Holdsworth, Richie Kotzen, Eddie Van Halen, Brett Garsed, Dimebag Darrell, etc., tend to be more legato. Picking fewer notes and making extensive use of hammer ons & pull offs.
Some dudes like Jason Becker, Paul Gilbert, George Lynch, Tony MacAlpine and Darren Householder, to name a few, would pretty much do equal parts of each.
Warren Di Martini used to employ a method where he would pick two notes and hammer on the third when he was doing an ascending run and pick the first note & pull off the next two on descending runs...mainly because that's what felt most natural to him.
Shawn Lane would sometimes use hammer ons, across the strings. He'd pick a note on the high E string, then hammer notes on the B and G strings. He would run those patterns up/down & across the neck...and he could absolutely fly doing that sorta thing.
This one dude (One That Taps) that used to hang out at the old Guitar Battle site...never even uses a pick. He does it all just by tapping and he could flatout rip.
So it's really up to you to find your own voice. There is no right or wrong way. As you go along, you'll probably find that one particular method comes more naturally to you than others do...At that point, you've just gotta decide, if it's giving you all that you really want...or if you really need to hunker down and tighten up your other techniques as well. You've got to figure that out for yourself and if it's right for you...it's right.
EVH didn't become EVH by feeling that he had to cop Malmsteen licks...
..and Steve Morse didn't become Steve Morse by worrying that his legato was not as good as Holdsworth's.
Try'em all & build'em up slowly and cleanly...then focus on finding what makes your playing "your own". In the long run, that'll serve you better than worrying about mastering the art of the shred. LOL :rock:
Don