ALICE
Pros: classic but very retro, nice sound, nice meaning ("noble"), most people know how to spell it, cute nn,
Ali
Cons: visually turns into 'a lice' (I'm sure no one else sees that but me!)
ANNE
Pros: has a long history, pedigree, nice meaning ("grace"), adorable nn,
Annie
Cons: it sounds rather plain, very common fn and mn throughout the years, just not very exiting to me because it sounds like an article of speech ('an')
FWIW, I say go with
Alice!