You didn't say what kind of anniversary - dating, wedding, etc. I'm gonna go on the assumption that you've been dating for a month - if that's wrong, then take this accordingly:
I would stay away from anything with the hearts on it, because that's pretty symbolic for most girls, and it reads as clingy after only one month. Same goes for lockets, unless you have something in mind to go inside that doesn't fall under the above.
The others that are shown there are pretty, I'd go for a lariat myself, but use your best judgement of what you think she'd like.