I'd pick
Anna. I like all three names, but
Hannah is too popular and
Anne is a little boring IMO. Also, I just like
Anna the best. I have never had a bad association with an
Anna.
If I used
Hannah I'd use the spelling
Hanna, and maybe the pronunciation that goes along with
Hanna (HAHN-ah) rather than HAN-ah) and if I used
Anne I'd call her
Annie. I do love the nickname
Annie.