See in my head, Babs definitely has a type. I think she had a few major relationships, right?
I think of dick as a thing that happened a lot on and off until the Birds of Prey where during an off period, Babs and Dinah became a solid thing. But he was a committed relationship to her multiple times pre and post Oracle. One of the breakups was definitely regarding Cass and Barbara raising her without talking to him about it.
Kara I really love as a Babsgirl era relationship. I think maybe dick was the first boyfriend first everything, but Babs looks back more often on Kara. They aren't like, bad ex's. They're lesbians ffs, they're friends. It just... Didn't work for whatever reason.
TedBabs... Honestly this one was between DickBabs and DinahBabs. It was fun, it was a thing, idk if she was committed. She probably enjoyed it but he's the one she forgets too. Jim probably doesn't know it even happened. Probably also an inciting incident for the break from Dick to fully Dinah/BOPolycule because... Oh. Fuck wasn't that great even as far as men go. Cool.
DinahBabs/BOPolycule is I think the end game for Babs. It's easy, it's clean, even if a guy or a girl or three come into their lives, it's the trust. It's the codependency without needing eachother there constantly. Dinah gives a life for Barbara that's amazing, and they understand eachother. Barbara keeps her independence too, but knows she has Dinah at all times. It just works for both, even if it's not traditional.
Edit: the type is blonde women. I'm saying that those are her highlights