The PPL syllabus is very prescriptive, dividing the practical training into specific exercises. Using FAA literature will likely create confusion and frustrate your instructor!
The theoretical knowledge also contains many EASA and UK specifics, so you want either the AFE or Pooley's books. Make sure you have the latest editions for Air Law and Operational Procedures as there have been several changes in recent years due to the adoption of SERA (Standardised European Rules of the Air) and the new PPL e-exam syllabus.