one of the Auntys that teach the FREE ukulele lessons at the Royal Hawaiian Center in Waikiki is Aunty Wainani.
She regularly begins with these chords, in this order: C, C7, F, A7, D7, G7. Then, depending on the song she plans on teaching, she'll move on to F7, Dm, Bb.
NOTE: out of the 60 minutes of the FREE lesson, she usually spends 30+ minutes going over the chords, over, and over, and over again. Why? Because no one can really 'play' the ukulele without knowing and being able to smoothly change from chord to chord in rhythm with the flow of the melody of the song.
anyway, I recommend the above series of chords as another Basic Chords Chart, for your consideration.
keep uke'in',
PS if you're ever in Waikiki, from Tues through Friday, and are free between 10 and 11am, please go to the Royal Hawaiian Center Food Court and enjoy one of those FREE ukulele lessons. There are generally 24 loaner ukes available, so go early and sign up... or bring your own! (BYOU)
Aunty Wainani teaches on Tues and Thurs. Aunty Puakeala teaches on Wed and Friday.