Yes, if you need/want direct SQLite interaction, FMDB is an excellent choice. It offers a simple and robust interface to the SQLite C API.
You might also want to consider Core Data, the iOS framework for "object life-cycle and object graph management, including persistence," which generally uses SQLite behind the scenes.
As the Core Data documentation says "Core Data is not a relational database or a relational database management system (RDBMS)." The Core Data Technology Overview clearly delineates precisely what Core Data is and what it is not.
Having said that, for many applications, it offers a number of advantages over interfacing directly with SQLite, itself, and its worthwhile considering Core Data before you simply dive into SQLite programming yourself.