I think
Jessie sounds like a nickname, when used in that spelling and for a girl. (
Jesse for a boy is another story.)
Jessica is nice, but somewhat dated and was way too popular at it's peak for my tastes. Needs a break.
Jessamine would probably get mispronunciations (I said it "JESS-ah-meen" at first.) But I like the name enough that it would not deter me from using it. I would most want to be called
Jessamine, personally. And I like the option of
Minnie as a nickname.