What music book (or books) should you choose when there are so many? Below are lists of books and resources put into categories with brief remarks.

This page is very much in-progress.

Piano Studies

Le Pianiste virtuose (The Virtuoso Pianist) by Charles-Louis Hanon. THE exercise book I use for all students. Contains finger dexterity exercises and scales. It is not necessary to do every exercise, but learning a few with good habits does wonders.
Beyer. Yes, I know that Beyer looks boring. It is certainly not suited for every student because this does require hard work and discipline without being encouraged by colourful pictures of dancing monsters or whatever weird thing is in the latest piano book.

Violin Studies

Melodious Double-Stops by Josephine Trott. This collection of short exercises for learning double-stops is what I go to when looking for exercises comprised only of double-stops. The “melodious” part makes it less mechanical and more fun than repeatedly drawing the bow across two strings in a single pattern.
School Of Violin-Technics (Book 1) by Henry Schradieck. For every violin student I have ever taught, I have always used at least the first page of this book. Use it to emphasize technique.
Scale Studies For The Violin by Jan Hrimaly. This is one of two books that I pull scales from for students. Frankly, I find myself usually using the beginning and the end, for the most part. The beginning has random techniques for each scale. The ending has all the scales written out in 3 octaves along with their arpeggios.
Franz Wohlfahrt’s 60 Studies for Violin, Op. 45. These etudes are frequently studied by beginner violinists, and for good reason. The second half, often sold as “Book Two”, is oft neglected but is equally good as the first half is. This was my first etude book when I was 7 years old, so I suppose there may be some sentimentality involved.

Sonatas and Partitas for Solo Violin by Johann Sebastian Bach. These etude-like solo pieces require dexterity of fingers, excellent memory, and musicality all at once. It is very apparent when you lack the ability to make the piece your own because there is no accompaniment to fill in and support you! It is remarkable! Mathematical perfection in musical form! (Of course, I have always loved Bach…)

The Suzuki Method for any instrument. The advantage of the Suzuki method is that, it being a method in part founded on the idea of listening, is that there are numerous recordings of the Suzuki books’ music online. I think that listening is important early on, but I try to focus on building a strong foundation in techniques and scales. The Suzuki method purely by itself is not always conducive to the scales bit.
Barbara Barber’s Solos for Young Violinists is a six-volume series helpfully organized by difficulty and has a list of what techniques each piece requires.