I've known one
Alicia, who pronounced it a-LISH-a. I think the same was true of a dancer called
Alicia Markova - I've heard her name said that way too. I'm South African, and the people I've heard spoke something very close to British English.
I don't know who
Alicia Silverstone is or how she pronounces anything - sorry!
I'd choose
Alice any time, then
Alison and finally
Alicia; I can't take
Alyssa seriously, though I once met a very nice one.