I would like to learn some jazz standards, but is there any recommended list to follow from easy to difficult? Because I am not very fast on the guitar, I want to know which of them are best for beginners. And also, should I follow the real book or the new real book? Or any other book than these two? I am a bit confused about it.
If you want to learn standards I would start by getting your hands on various versions of them being performed by great musicians. This is the best way to learn music, and style of music. Listen. If you can listen to the original versions. This should be an easy task with YouTube. 20-30 years ago I'd make a mixed tape, or burn a CD with 12 or more versions of a some I wanted to learn just to get a feel for the variety of ways it could be played.
As for complexity or difficulty? That is hard for others to judges for you. You say you are not fast but speed is not the only thing that makes a song difficult. Some tunes are fairly simple from a changes perspective while other are a little more difficult to analyze.
I would recommend the Real Book 5th ed, and the second volume. I got mine back in the 80s and it has served me well. I've read through about a dozen so call Fake Books and I think the Real Book has pretty good changes, even if not 100% accurate. Another reason I recommend it is that there is a free version of the Real Book files out there somewhere for Band in a Box and that is great to play with. You could also look into getting a couple Jamey Abersold play along CD's (or whatever the technology is today). The Abersold collection is pretty good. You get backing tracks for anywhere from 10-20 songs and the lead sheets. You can specifically get beginner level material, i.e. "easy changes", then work your way up to harder ones.
From the Real Book here are few tunes that are nice and have easy to digest changes.
A Foggy Day
All Of Me
Night and Day
There Will Never Be Another You
You Don't know What Love Is
Then work up to the following...
All of You
Autumn in New York
Body and Soul
Darn That Dream
How High The Moon
Stella By Starlight
West Coast Blues
In my opinion the first set has simpler melodies and fewer changes while the second is a little more involved. That is just my opinion though.
In addition to ggcg's great list, I'd add these basics/staples:
- Billie's Bounce
- Blue Bossa
- All the Things You Are
- There Is No Greater Love
- I Love You
- On Green Dolphin Street
- My Funny Valentine
- Recorda Me
- Satin Doll
- St. Thomas
- Take the A Train
- So What
- In A Sentimental Mood
- Alone Together
- Fly Me to the Moon
- I'll Remember April
- Just Friends
Here are some more advanced songs that you could work toward. They're a little harder but still highly common and among the most-played standards:
- Days Of Wine And Roses
- Have You Met Miss Jones
- Girl From Ipanema
Kudos to @ggcg and @ jdjazz. Both of their answers and lists are excellent and represent a body of American songbook and jazz standards that all professional jazz musicians know and all serious jazz students should work towards learning. I am going to offer you a much shorter list of songs taken from these other two which I think have a lot of the basic elements that jazz students need to learn and understand and a brief explanation of those elements:
Satin Doll (great IIm7-V7-I practice)
Take the A Train (one of many songs with a II7 chord; also a song that has longer durations of individual chords for learning how to play longer lines over a single chord)
I Got Rhythm (not on these lists but many jazz standards like Oleo are based on this song’s harmony; The bridge offers good practice playing dominant chord cycle of 5ths)
All of Me (a fairly easy song to learn, lots of secondary dominants)
Autumn Leaves (excellent use of relative major and minor keys)
Learn and memorize the melodies! Ask yourself why they work so well. This will help you develop a good melodic sense for improvising and writing your own songs one day.