Method/Material choice is highly dependent upon the age, goals, instrument, and personality/temperament of the student.
PIANO: Generally speaking, for a child beginner student, I'm using either Bastien or Faber and Faber. For 12+ year old piano students, beginner through intermediate, I often work from Alfred's All-In-One piano instruction book, supplementing with appropriate pop, classical, and theory work as the student progresses. I have found Practical Theory Complete, by Sandy Feldstein, to be an invaluable resource for both piano and vocal students.
I often teach adults who are beginning students or are coming back to piano after an absence. We work together to tailor the repertoire to their desires, which are often just personal fulfillment. Coming back to or being introduced to musical study as an adult is immensely rewarding, and it is a great joy of mine to be able to correlate the life experience they have with the study of the arts.
For more advanced students, teenage to adult, I develop an individual curriculum/repertoire plan based on need. If I am preparing middle or high school students for conservatory or university entrance, we study a rigorous blend of scales/technic work, music history and theory, and a balance of difficulty-appropriate classical pieces from all time periods. We study on the semester program, in preparation for their university schedule.
I often work with older students on the development of playing by ear - understanding enough music theory to learn basic chording patterns, and then growing into skilled performers of popular music or their own arrangements.
VOICE: For students from 8-13, vocal instruction is focused on confidence building and a proper foundation for singing. I use a combination of well-known children's songs, such as in Hal Leonard's Essential Songs series, the children's book, and songs from their favorite artists. Through these songs, students learn to sing out strongly without shouting, form their vowels correctly, hold out the vowels of each word and create long vocal lines, and communicate emotion through song. These basic studies prepare the student for a future in voice without the technic work and more rigorous study that they aren't ready for physically. I try to expose each student to styles of music they might not be familiar with.
For teenage to adult students, as with piano, the approach is tailored to individual need. Many teenage students are looking to express themselves and better their "instrument", but are not focusing on university level music work. We still focus on a well-rounded approach to music and the arts, but with a less rigorous plan that seeks to discover their vocal strengths and feed the musical itch within them.
Often adult voice students are looking to fulfill a desire to study voice that has been in the back of their minds for years. I work to explore and fulfill that desire through whatever genres of music make sense for their lives. Many times, I see adult students with significant natural gifts that need my help refining their sound for performance. I have taught many worship leaders, professional performers, teachers, and local singers who are looking to branch into national work or simply learn correct vocal technique to protect their voice from its daily abuse.