Luna Lovegood is a very difficult character to portray. She's easily one of my favorites in Harry Potter, but she is a complex person.
Luna is not self-conscious in the slightest. She is rather independent in her beliefs and her thoughts. Luna has never cared about people's opinions of her. Nonetheless, she's always been a bit of an outsider. She was ecstatic to have Harry, Ron, Hermione, Ginny and Neville as her friends, as we see in DH in her bedroom. Her nickname, too. 'Loony Luna'. She also has possessions taken from her throughout the course of the year, as we learn in OOTP.
No one can deny that she is not intelligent, though. She might of been a little like Hermione (pre-Ron and Harry friendship), involved in reading and the like, before the DA. Even though she knows about things other wizards and witches doubt are real, she knows a lot. Luna is pretty insightful too. She's also rather curious. That might be a trigger for how she knows so much, do you know what I mean?
Luna isnt afraid to speak her mind. She'll tell you what she thinks, straight-out. She's a pretty pleasant person overall. She's very optimistic and strong-willed, one could say, because she doesn't let anyone sway her opinions on things like Crumped-Horned Snorkacks and Nargles. She's also vert close with her father and happy with him, although she must miss her mother. She still keeps a picture of her and her mother on her bedside table.
Now for your questions.
How would she act in a relationship and how would she react to romance advances?
I'd think she'd act like it was a friendship, mainly. She wouldn't be the kind of person to know at any lengths to please her boyfriend or be flirtatious and such. She'd be kind of calm about it. She wouldn't worry about romantic advances because she wouldn't go loopy about a relationship.
What would her 'type' be?
She'd probably like someone intelligent. They'd have to be open-minded to her beliefs and thoughts, for sure. They'd also have to be a good friend to her. Those are just my thoughts though.
Hope I helped!