Jessie as a full first name just seems lazy or thoughtless to me. And I don't really think it grows up well, even as a nickname.
Jessica is pretty much as classic as
Jessie, and I think it ages well. The hostess of our creative writing group is named
Jessica, and she is 68 or 69, so I can definitely see it aging nicely.
Jessamine is cute and different but it doesn't do it for me like
Jessica does. If worrying about how it's pronounced by others bothers you that much, you could spell it
Jessamyn.