Harry/Hermione/Ron had a solid friendship. I think that Harry and Hermione could have been pretty good together, romantically speaking, but apparently they weren't ever in love with each other, so that's that. With Ron and Hermione, Hermione was significantly ahead of Ron in terms of emotional maturity, and then she noticed "Oh shit, I think I'm falling in love with that idiot" while Ron friendzoned her and refused to even consider thinking of her in that way. But Ron eventually came around and allowed himself to think of her as more than a friend, and embraced the truth, which was that he was already in love with her and had been for some time. I think people who say that Ron x Hermione would never work are being unfair to the two of them. I think they could make it work.
Harry x Cho didn't work because Cho was on the rebound and emotionally messed up (and it probably didn't hurt that Harry was the Chosen One), and Harry's attraction to Cho was superficial. Their relationship was doomed after Cho's BFF betrayed Dumbledore's Army, and Hermione sniffed out the traitor by suspecting everyone, and Cho blamed Hermione for not trusting Cho's BFF. Harry's like "We're trying to fight A WAR here, what part of that don't you understand?" Harry can't be with anyone who doesn't take Voldemort deadly serious, which is part of why he's OK with Ginny.
For Harry x Ginny, Ginny was mostly a background character, but she had a target lock on Harry since she was 10 years old, before anyone even knew who Harry was, and the stuff he did with becoming Ron's BFF and being the Chosen One only shot him up in her estimation. She played the long game to land Harry and frequently got advice from Hermione. She dated a guy who she specifically viewed as a stepping-stone. Don't get between Ginny and her Harry or she will cut you. I entirely don't see Harry being in love with Ginny, but Harry's shallow, and Ginny ticks off some checkboxes (she hates Voldemort with a passion, check, she acts as an entry point into Ron's awesome family, check, she's cute, check, she wants to marry Harry, check...).
Harry x Luna is pretty good.
Luna x Neville is even better.
