Hi! Have you named her yet?
Congrats on your new kitty!!!!!!!!!!!!!!!
Did the vet say how old she is?
If she's somewhere around three months, she is VERY likely starting to teethe. This is the bitey stage, and it is imperative that no one plays with her with hands or feet (though it is tempting because it's cute).
Blowing on her and saying "no" is exactly the right thing to do. Her mom would hiss at her (or lightly bonk her on her forehead). Just be very consistent about it.
But whether she's teething or not, because she's got this "chewing" thing, the very best thing to do is buy a box of bendy straws and scatter like half the box around so they're easily within reach.
With kitties, it's important to redirect improper behavior to proper behavior, and to provide positive reinforcement along with the "no's."
So when she goes to bite toes or fingers, blow in her face, say "no," pick up a straw and give it to her, and when she starts biting on it, say "Good Girl!" and praise her a lot. If she ignores the straw and goes back for fingers or toes, blow again, say "no" again, give her the straw to chew, and walk away. If she consistently gets ignored by this behavior, she'll learn pretty quickly it's no fun doing it.
Also, at some point she's going to want to scratch stuff, so it's important you have appropriate stuff for her to scratch on. Being new to cats, PLEASE do not even consider having her declawed. It is illegal in 23 countries around the world because it is cruel. It's not like removing fingernails. The claws, which are retractable, are attached to the toes in such a way that the last joint of the toe needs to be removed in the process of declawing. Cats actually walk on their toes, and it can cause both health and behavior problems (esp peeing outside the box).
So make sure you get some scratching posts and a vertical cardboard scratcher or something. She's probably a little young to want to scratch yet, but she'll want to soon enough. The best place to put them is somewhere where she likes to nap - because cats LOVE to scratch and stretch when they wake up.
As to the shoulder thing? Hubby would be completely and entirely jealous of this. I suspect it's that she likes to be "up". Cats are animals that like to go vertical - so providing vertical space is important for them. They love the backs of chairs, couches, tops of bookshelves - stuff like that. If you have room and can afford it or can or want to build one, having a cat tree (or trees!) around for kitties is always a good thing (Right now we have more cat furniture than people furniture!
). Gives them something to climb and hop around on.
We saw a guy at the vet walk in with a kitty just sitting on his shoulder. Gary asked - how did you get her to do that? He said - she just always did it on her own. She was like a parrot or something! It helped that she was a little kitty. But it was terribly cute.