I think you need to remember that you're not actually naming a baby - you're naming a person who will spend a tiny fraction of her life as a baby, a fairly small part of it as a child, and then possibly 80 years plus as a grown woman.
Apricot - I think it's awful, but I can just about see how you might think it would suit a cuddly, round, dimply little baby. But imagine it on a 6 foot tall soldier who runs ultramarathons in her spare time - it doesn't work so well, does it? I've known three people with fruit names, and all hated them, with two changing them as soon as they were allowed.
Venus - probably the least awful of the batch, but it's a lot to live up to. I think people will think of the goddess of beauty first, and Venus Williams second.
Story - I don't like it, but if you really have to go with something that's not usually a name, it's not offensive.
Ember - awful. A burnt-out piece of wood. Dying embers. Ashes. Really miserable connotations.
There are a lot of lovely, unusual names out there. Like someone else said, it's not a binary decision between top 10 name and not-actually-a-name.