Just some quick thoughts along the same lines as Paul and Robert...
First, memorize everything Robert said.
As for the alternation, I fully agree with Paul. However, you'll notice on my vids, I don't follow the left hand fingerings exactly either...there's a reason that I'll get to in a sec.
Before that, let me explain that my formal guitar education is a bit spotty, at best. Although I've played since I was 5, I only had a few months of formal lessons. Fortunately, some of those involved fingerstyle guitar, which I fell in love with. Additionally, after high school, I stopped playing...for about 20 years.
The little bit of formal music education I received was through the school band (trumpet) for 6 years. However, I only took a few lessons each year before a major competition.
Where was I going with this? OH!!! Alternation!!!
Most of my guitar playing until very recently was limited to fingerstyle...I very RARELY played with a pick. However, I decided to learn to use a plectrum earlier this year. As with fingers, alternation is key to developing speed and accuracy. However, I taught myself the "economy of motion" method FIRST, before truly developing alternate picking. As might be expected from more experienced players, my speed was VERY slow...and inaccurate.
THEN I focused on re-learning alternate picking...the "right" way. It was very challenging at first...and slow. However, especially with the help of a metronome, my speed quickly increased and soon surpassed my previous limits by about 50 bmp. I still can't "shred," but I'm a heckuva lot faster...and really in a short amount of time.
So, in a word, "yes," alternating fingers is pretty critical. And START SLOWLY...40 bmp if needed. Use a metronome. As you slowly increase your speed, you'll be able to SEE improvement.
Now, so why don't I always follow this? Well, along the way, I also taught myself electric bass guitar. I used several resources, both in print and online. Economy of motion and the rest stroke are stressed by bass instructors fairly widely...and that's what I learned.
For example, in our setting, the "i" plays a note on the high E string. Using the rest stroke, the "i" comes to rest on the B string. Economy of motion...and my background in bass guitar...would have the "i" play the next note (on the B string), rather that alternating with the "m."
I have a very hard time with this...and it frustrates me to no end...as with alternating picking. I'm forced to relearn what's been ingrained through my 3 hr. daily practice sessions...and I know my speed and accuracy are suffering. Fortunately, I really don't use the rest stroke very much and opt for the free stroke. However, I think one should learn both...and the correct way to begin with.
One more thought and I'll close...string muting. Kudos for this being stressed so early...as it should be. Again, being self-taught, I never placed much emphasis on this...and my articulation suffered for it. I think this is another critical skill in a player's development, regardless of genre. Yet, string muting seems to be an afterthought to most tutors, if it's mentioned at all.
If you proceed slowly...at an absolute CRAWL...use a metronome...MAKE your fingers alternate...go so far as to continue the fingerings on the entire piece in pencil...mute the strings, ESPECIALLY during the rests...you'll engrain yourself with the proper techniques from the start...and not have to relearn.
Oh...one other thought...in addition to following Delcamp's practice schedule...USE A TIMER. 10 minutes on a difficult passage? USE A TIMER. There's something about "being on the clock" that clicks the brain into a different gear. Try it and see for yourself.
"It is common sense to take a method and try it. If it fails, admit it frankly and try another. But above all, try something." -Franklin Delano Roosevelt, 1932