Hi and welcome!
So, just wondering - age, gender, orientation, etc. of you all???
There are a few threads here about introducing lovers to each other. I think the tags are "introductions" or "introducing lovers." You could also look for "vee dynamics" and thinks like that. Anyhoo ~ as I read your post, I thought maybe it would be good to invite them both to have coffee with you and meet before the actual party, to lessen any awkwardness.
For the party, rather than just inviting them and then fretting about what the outcome will be, just ask them if they even want to go. You could simply say, "So, I'm having this party and I'm not sure what to do. I've never been in this position before. I'd like to have both of you with me, but I don't want anyone feeling uncomfortable. Do you want to go?" And if there are issues raised, discuss them. Ask them what would make them feel more comfortable.
As for how to introduce them to other guests, you could just introduce them by name or as a friend. If you haven't been going out for very long, you might not be serious yet, so "friend" usually works. But how you handle that would depend on your audience (the other folks you invite), how "out" you want to be, and what your lovers are comfortable with. How uptight or receptive do you think your other party guests will be? Again, you could just talk about this with your lovers - "How should I introduce you?"
Regarding who stays over, you have a few choices: Person A, Person B, Both, Neither, or Someone you pick up at the party.