Inviting to a private drinking party?

I am from Europe and currently study Japanese and like that have been able to get into contact with several Japanese people.
Now I've been to a party at a Japanese restaurant where I got into a talk with a japanese exchange student. We chatted for awhile and at some point, the topic of drinking came up. I said that I had ordered "sake" to which she responded that she loves sake.
I told her that I like to drink it too and that I still have a bottle at home from my birthday. She then said something to the effect of: "hey cool, you can invite me, then we can drink together". She also gave me her mail address.

Now, the question is what to make of that or rather, how to go about it.
- Should I invite her to me home or rather choose a restaurant or something?
- Should I invite other people, like some of her and my Japanese friends along?
- What to do besides drinking? There will certainly be alot to talk about, but that's not enough for a whole evening i guess. Also, my Japanese is not particularly good yet.

Maybe those are strange questions, but I was rather surprised by how direct she was about wanting to be invited. I'm just not sure how to deal with it. It's also not that I expect anything sexual or dating-like from this, I just want to have a nice evening and figure out what she's up to...

So, any suggestions on what to offer her?

Wow, that is surprising to see how direct she was about wanting to be invited, and I'm just not sure how to deal with it either. Maybe it was just a joke??

In any case, as a courtesy, why not try contacting her for starters. I don't think you have to be specific about that sake bottle at your home. You can have it for yourself and joke about it to her like, "Oh, I accidentally drank all of it, ha ha" or something.

The email address can even be fake, but if it's not, she probably wanted to be friends with you. You can proceed any way you like from there.

Thanks for your very quick answer, Uco, I appreciate it.

Maybe it was a joke, I can't really tell. But considering we left the restaurant with me saying ''I'll contact you about the sake drinking'' and her responding with ''I'm looking forward to it'', I doubt it. Also, here mail is real for sure, because she's a student at my university and I could easily get the address from elsewhere, like from some of her friends who I already had contact with.

I will probably contact here soon, though I'm not sure yet how to go about it. I think maybe I can invite her and some other friends over to get something nice to eat and to drink the sake.