The only other girl I can remember Jason liking was the prostitute from the club. If that's not her, then I'd need to look it up because while I've read them all (I think so, anyway), I don't own them all.
Having done both, I do have a Steph/Tim preference myself for the same reason I love Babs/Dick. It's dysfunctional but loving and although sometimes they treat eachother like crap, they get through. I'm not really a Rose fan, but I'm on the Jason/Mia train tentatively. I do usually prefer gen stuff to romance (especially with Robins and Speedys) but I like it enough.