Modern Guitar Method, Mel Bay; Guitar Volume 1, Hal Leonard
These two books are the most popular books for beginner guitar students. Mel Bay has been the go to book since 1948. Not only does it introduce the notes in the first position, but it also exposes students to playing solo arrangements of songs. After going through single notes on all six strings, students learn to how to read and play chords that are written on the staff. Hal Leonard introduces the notes, but does not get into solo arrangements. I think that both books work well together. It's important to be able to read single notes as well as chordal arrangements. When used together, the books compliment each other well.
A Common Sense Approach to Improvisation, Joe Negri
Mr. Negri's book focuses on playing triads on the D, G, and B string. He goes through all twelve major, minor, and dominant chords in root position, first inversion, and second inversion. Going through this book helps students to become very familiar with the fretboard and all chord voicings. Exercises are included to help students to connect the triads in a melodic manner.
Mickey Baker's Complete Course in Jazz Guitar: Book 1, Mickey Baker
Mickey Baker put this book together with the goal of getting the student able to play "hot" jazz guitar in one year. There are 52 lessons, which Mr. Baker suggests that the student practice an hour a day for a week. The first half of the book focuses on rhythm playing. Students are introduced to common jazz chords and chord voicings. The second half of the book focuses on soloing and the "hot guitar" vocabulary. Students are first introduced to some scales, then work through several guitar licks that are transcribed for the student to play.
Blues Guitar; Country Guitar, Hal Leonard
Hal Leonard has an excellent series on playing different styles of guitar, and the Blues and Country books are my favorite two. The books go through varies techniques of each style, for playing both rhythm and soloing, having the student work through songs. There are licks transcribed "in the style of" different guitarists of the genre. These books really give a student a feel for the language of each style of music.
Classic Guitar Technique, Volume 1, Aaron Shearer
When I was in college, I took some Classical guitar lessons, and this is the book that the instructor used. In this book, students gain the necessary technique for playing Classical guitar. I believe that it is important for guitarists to have the ability to play with a pick, play finger style, and hybrid pick. I use the exercises in this book for finger style and hybrid picking.
I hope that these recommendations help you on your journey as a guitarist. Please feel free to comment on what books you have found useful on your path!