Starting a new business with a partner and I'm a little spooked

I am starting a business with another person. The entire thing is my idea from soup to nuts. My partner has made very few contributions in terms of the concept or how to execute the whole thing, but I need her because she has a very highly specialized skill, so I'm willing to split it all 50/50 with her.

I briefly told her my idea and she was really excited - then we met for dinner to discuss it at length and she's totally on board. But I got a little spooked because she started talking about how her brother can help with this and her sister can help with that, and she already owns a business and can make this a subsidiary under her business, and she might already have some funding, etc. I *think* that she's just overly excited, but as our conversation progressed it dawned on me that I basically just gave this woman the keys to the castle and I have no protection at all.

So I feel like I need to ACT FAST and protect my idea. I plan on getting a non-disclosure agreement and a partnership agreement for starters. Should I also form a business now, and if so, what kind (LLC, LLP, S-Corp)? I tried looking up the differences between these company types but I really don't understand them well or how to tell what applies best to me/us. Is there anything else I can do to protect my idea?

Thanks for your help.