One word - metronome! Pushing yourself harder with a couple of extra bpm every few minutes works wonders, plus you can keep an objective record of your progress.

Personally I don't use a pick very much because they make me feel a little "detached" from the guitar, but I can get some pretty fast runs going with just my thumb and middle finger, using a combination of picking and slurs. I would recommend practicing everything on an acoustic guitar or with a clean tone through your amp (or unamplified) - it really helps you focus on your accuracy without using distortion as a crutch.

Every guitar teacher/properly trained guitarist on here is going cringe at this but I HATE metronomes and feel that in many ways they can be quite limiting while learning. They can also make a player too rigid to follow a live drummer or kill the little timing fluctuations that can add some feel to one's playing. It certainly IS important to be able to play in perfect time and being able to have benchmarks to set for oneself while learning scales but while the scales/licks/techniques are actually being absorbed I've always found it much better to learn the material, hack through it until it is second nature THEN force it into robot time.
 
That philosophy has however really screwed me up now that I'm working with MIDI and click tracks in the studio but I'm getting over it. I can keep "time" with whatever wacky drummer or other musicians through sheer feel though which was far more important during all the years of drunken bar gigs.
 
Learning scales/arpeggios with a clean tone is a very good idea. Hi gain can compensate for poor technique and it does indeed become a crutch. When you have good technique to start with THEN apply the crunch... well that's when you get the Danzi style articulation. I used to be able to play that clean but years of abuse on my hands (construction jobs and generally being an angry smashy guy) coupled with an unfortunate physical ailment has made me a little sloppier so I have to try harder and pay more attention.
 
I however like a little skankiness in my music so it ain't so bad.

This is great stuff guys!  Thanks so much.  I don't understand half of what was said so once I get to my Strat and start reading these posts again, I should start to understand better.  
It's all good.
 
Rimshot

Along with Beepsters excellent advice, be sure that Strat is set up properly.
There are few things more frustrating than fighting a guitar with too-high action.

OK Part 2 but first ..TACOS!

YUM! so..
Part Deaux - I will refer this series of Left Hand exercises as finger rolls. index= 1  middle=2 etc.
You want each finger to come down firmly just behind the fret but not overly forceful. Give each finger equal force so the string clearly sounds the note. no 2 fingers down at the same time. These are triplets so are 3 finger rolls. USE A METRONOME (1st finger down gets the click) 
Start and stay at the 5th fret on the G string.
1) roll fingers 1 , 2, and 3 in a triplet pattern. 123123123123123123 in one direction on 5th 6th and 7th frets. Try to stay relaxed and pick a slow to medium tempo. I'd suggest a tempo of 120 to start with. Try non stop for one minute
2) roll fingers 2,3,and 4       234234234234 etc.
3) "      "        124124124124124etc
4) "      "        134134134134134 etc
 
Focus (close your eyes)

Next reverse 1-4   321321321/432432432/421421421421/43143143

Gradually over time build up your speed
 
Part 3 is adding the pick to the mixture accenting the 1st note in the triplet. This will build balance with up and down strokes. Next accent with the pick only(left hand doesn't change) the 2nd note of the triplet. Ex. one - TRIP - let two TRIP - let etc. then the 3rd note (one - trip - LET etc.)
 
It's to start your practice with these exercises. Stay with this at least 2 months and try to do it daily. It doesn't take long. This is part of my daily warm up routine. It will give you results
 
After a few months use fingers 1 2 3 4 in 16th note patterns. That's Part 4 
 

 

I need to add something on left hand muting to these exercises. When you place your fingers on the string slightly touch the 2 adjacent strings above and below so they are muted and don't sound a note. This will help immensely when you get into fast tempos if you start left hand muting now. That way when you are alternate picking your free to accent as needed with your picking hand without any unwanted notes or sounds. Also, there shouldn't be any pressure applied with your left hand thumb on back of the neck. 

I would say, find a song with a part (or parts?) that you like, pull it in, and slow it down... Then study those parts. You can take anything anyone has done, and slow it as much as you'd like. You lose sound quality? But you can use this as a tool to figure things out. I'm sure Cake can do this, but I use soundforge and then import in to Sonar. It's a great tool for figuring out how things work. You can combine this tech with controlling the stereo field as some parts are in the middle, and other things are on the sides and using EQ. Then you can practice with it at a slower (much slower) speed, and dissect what is going on. You can combine this with people on youtube "showing you what is going on." With the combination of these techniques "and time" there is no limit to what you can achieve. You are limited ONLY by your imagination. 
 
Pull up a youtube video of Tony Rice and his all star band playing the bluegrass guitar ;-) At regular speed, "it's difficult to follow?" I watching this one earlier, and remember, they're playing "live?" No tricks...
 
https://www.youtube.com/watch?v=_u964a0f38s
 
I understand the musical style may not translate? However, the fact remains, theory remains, practice, speed, skill and talent, etc.

MakeShift
Jimmy, I'm waiting to see if any Danzi video training videos pop up. 😄

LOL! You mean I may actually serve a purpose somewhere? Who am I kiddin' :-)

You bring to the table more than you will ever know Brother.