When it comes to sex / sleeping / other bedroom activities in the world of poly there are many options, and many different configurations and answers that you'll get if you ask anyone what they personally do and how they personally arrange their relationships.
I do agree with other posters that the 'unicorn' fantasy does not generally work out. I have never been one for black and white thinking, so I am sure that somewhere, somehow there is a unicorn relationship that has worked out, but of the very few that I've seen, none of them have worked out longer than a few months.
I think, and of course I've not had firsthand experience, because my relationships are not of this variety, that the unicorn fantasy compartmentalizes the relationship too much, and doesn't allow for growth. It has never appealed to me personally because a couple looking for their unicorn to me seems like they are looking for a toy, or a possession rather than a relationship. Granted, I could be wrong, but this is just what I've observed...
That being said, sex does tend to happen in poly relationships (and all others, of course); There are nine people total in our poly family between my husband and I and our partners and their partners, and I have sex with three of those people. We don't require that everyone's partners have sex with everyone else. We allow everything to ebb and flow naturally and to move at the pace it will.
My advice is that in your particular situation, write down or discuss exactly why you are seeking the third partner. What reasons do you have? Does it have to do with sex primarily, or companionship? What benefits would you all three gain from this partnership?
Please know that I'm definitely not trying to be a party pooper or a naysayer; it just sounds like your goal is slightly unrealistic as of yet. That's not to say that it will be that way always. If you're new to poly, you have the opportunity to learn from those around you, explore your own motivations, do some self-work, and fine tune your goals and desires to what really works for you, and the other person that may potentially come into your life.