As Stephen Sawall says above :but adding to it;
The Tortex picks for example, are low on pick noise due to the material - and using .88 and 1.0 or larger since the rounded edge" wraps around the string" if you use the correct angle , and subtle circle picking, lessens noise even more.
As these picks wear they get a little edge ( and sound like a thinner gauge )- you can light sand them back with 320 paper to re- round them.
Practice on one note alternate picking and get the upstrokes and downstrokes to sound the same ( and being able to accent either one ) and exaggerate the attack like a Flamenco Player then back it off to smoother and smoother. Slow and fast ( called Tremelo Picking like mandolin players do and EVH used to in some solos ).
You are controlling depth of the pick into the string-( how hard you pick), and the pick angle- eventually you just "hear it" in your mind and there's no thought about it- gets automatic.
I have my pickups set far from the strings so if I pick softly ( not digging in very hard ) at higher speeds- it can almost sound like tapping- but if I pick hard you hear the attack, but still very little "clank" at the beginning of the note unless I really nail it.
Players who mostly pick really hard sound better on Acoustic IMO because the heavy percussive attack with gain through an Amp can be harsh IMO as opposed to players like E J, Gilmour, Timmons, who use a more "bowed " attack.
Delay tends to soften attack on your Leads- and of course an Amp or Preamp that has a little "sag" also softens attack, as do Tube Pedals like Chandler or Butler Tube overdrives, Radial Tone Bones etc - even with subtle gain- but best to get it with your Fingers ( controlled picking attack), mostly IMO.
Elixir Coated Strings soften a tiny bit more, as do other warmer toned strings once you have the above stuff really together( but this is very subtle, but good for Recording IMO).