Is it weird out of the blue someone offers you a job from a first meeting!?

I'd be wary, but it could be legitimate, particularly as you actually spoke face-to-face (many scams these days are on-line or via the telephone). It also depends upon the type of job, and the type of business she operates. An independent business owner often makes rapid hiring decisions.

Wait to hear more and then judge for yourself if it sounds legitimate and something you'd like to try. I wouldn't be overly worried about giving just your name and phone number.

I'd be wary that the "job" is actually an MLM "opportunity".

With an MLM, they only require that you be breathing. Apparently, you passed that test.

If you join an MLM, you would be asked to sell products and recruit others to do the same (like she did with you). However, as the products tend to be overpriced, they are very tough to sell and it is always tough to recruit people. As you will always be recruiting, your friends and family will start to avoid you like the plague. People who you have known for years will literally jump out of windows to avoid talking to you.

Most people who join an MLM end up actually losing money. The drop out rate after two years is over 90%.

It is very weird. On one hand, she could be from an employment agency and she's just looking for a client. On the other hand, I don't know. Wait until she calls you and see what she says. Who knows, it might be a good thing! If not, change your phone number. Hope this helps. Good luck! :)

To be weird something has to be unusual. Scams like this are too common to be weird.