Q:"I have been practising classical guitar for the last 3 years, so I know more or less what it is all about - and no, I don't want to sing - I want to play fingerstyle :) Are there any old books/methods that I should follow, or should I just download the arrangements and start working on them?"
A: There is no correct answer to that question, but I can tell you what _my_ approach would be for anyone wanting to get into fingerstyle.
Classical is a great place to start, it is fingerstyle after all. Be able to fluently play basic classical pieces - bass notes on beat with a melody. Classical will give you the left and right hand skills required for any future sort of guitar playing. Definitely get some lessons to start with so you can pick up good habits in the early days.
One of the songs I play "Here Comes the Sun" is an example of a "classical" styled piece. It was one of my really early crossover pieces from classical to the style I play now.
You can keep following the classical path forever, and it will continue to challenge and amaze you, but let's continue.
The next step I'd take is to try an alternating bass line piece. Anything by Chet Atkins, maybe have a crack at Freight Train, a well known alt bass starting point. Watch somebody play it on youtube first - the trick with alternating bass lines is generally every beat in a four beat bar the thumb plucks out a repeating bass line which, ahem, alternates :) Meantime the fingers are playing a melody. Alternating bass lines will help you develop good thumb skills, and a spatial awareness you might not get in "normal" classical playing. Being able to move from random string to random string with your right hand rather than following normal classical style patterns is another good skill. Alternating bass line is of course a pattern, but not one generally incorporated into classical.
Again, you can follow the alternating bass line style forever, many people do, but let's keep going.
Rhythm guitar is important. Knowing where all your chords are, in lots of different positions, and being able to jump to them without even thinking. Play chords along with songs on the radio - helps with another good skill of getting your ear tuned in to music. That is part of the whole "learn music theory" road which personally I haven't done enough of. I've developed a bunch of skills but I don't have the music theory to back me up. Learn about music, you will need it at some stage.
Some Flamenco style will help out with fingerstyle; let's call it optional, but I find Flamenco has an underlying influence on fingerstyle for me. Solo shredding could also be another helpful influence; not really my cup of tea, but we've all dabbled with it and it builds skills. Jazz, blues - the list goes on.
The real secret comes from I believe what is loosely described as "thumb independence". What that means is it looks like your right hand thumb and fingers are doing stuff separately, that is, independently. It will really strain your brain trying to get your fingers to play that crazy mixed up varying "off beat" to your thumb. It happens somewhat in alternating bass line style; but there are usually easy beat "hooks" present in alt bass; something that helps keep your brain "on track". I've written about thumb independence a few times, for instance here. I give an example of two seemingly "simple" bars of music that will really show you what thumb independence means. I don't think it was until I mastered those two bars (which required at least some of the background skills I mentioned) before it really dawned on my just what thumb independence consists of. Try it, if you can!
So the final phase is to learn some thumb independence songs from tabs. By rote, painfully, note by note. Choose a favourite arrangement from youtube; Tommy Emmanuel, Michael Chapdelaine, Naudo, Kelly Valleau, Ulli Bogershausen or Igor Presnyakov all have some great arrangements sometimes with tabs available (do an internet search, or try here). Once you've mastered some tabs, next try to transcribe some songs by others (Naudo and Igor would be prime candidates). Transcribing is difficult but you will learn a lot about how to piece together a fingerstyle song.
Finally, begin arranging your own fingerstyle covers (or creating your own compositions). You will have a wealth of skills and experience to fall back on, the sky is the limit! I've written about arranging before here.
Good skill to you in your fingerstyle journey!