I would prefer
Georgiana over both
Georgine and
Georgina, but if I had to chose between the two, I would go with
Georgina because it lends itself to the nick name
Gina.
How do you pronounce
Georgeta? It sounds awkward when I say it aloud, so I would go with
Georgette, which isn't a favorite either. Between
Georgine and
Georgeta, I prefer
Georgine because I could at least go by Jean/Gene.