I don't mind
Anastasia but I think it sounds a bit too princessy and frilly. I also think of the singer
Anastasia.
I say it "ana-STAY-ze-uh" but some say "ana-STAH-zyuh" - I haven't heard it pronounced your way but I prefer it to "ana-STAH-zyuh".
I think Nastia is a strange nickname, which I would avoid - it looks like the word "nasty" and sounds (to me) like "nastier". I would use
Ana or
Ania as a nickname.