Although there are buying guidelines in terms of age, grade level and self-administered diagnostics for individual AoPS books, here is a quick way to get started:

For middle school students, consider the Introduction Series - Introduction to Algebra, Introduction to Number Theory, Introduction to Counting and Probability, and Introduction to Geometry, and their corresponding solution manuals. They provide a terrific foundation even for advanced students.

For high school, consider the Intermediate Series – Intermediate Algebra and Intermediate Counting and Probability, and their corresponding solution manuals.

For acquiring the essence of problem solving, The Art of Problem Solving – Volume 1 is a must have for middle/high school students. For advanced high school students, The Art of Problem Solving – Volume 2 is a great purchase. The solution manuals are handy accompaniments. The Art of Problem Solving – Volumes 1 & 2 (with solutions) are also absolute must-haves for preparation for math competitive events.