I went with a Hal Leonard method written by Lil Rev when I wanted a book for my daughter. I didn't play uke myself, so I didn't know what to look for. In hindsight you probably don't need a book. There is so much stuff available online, on various websites and YouTube. Much is for free, especially for a beginner.
That's not to say that a book is useless, and that the Lil Rev one never got used. As a matter of fact, the book first got into simple melodies instead of a C or am chord. I already came from a 'melodic' instrument, and picking a melody line came easy to me. As a result I was never intimidated by fingerpicking, and I learnt that right from the start. If you know which music they listen to then you could try to look for 'easy X or Y for ukulele'.