How does Jane Austen demonstrate that 'romantic' love should be privileged over other types of love in the novel? What are some examples of this?
The main problem with this question is that Jane Austen is not a Romantic, and Pride and Prejudice is not Wuthering Heights or one of the Gothic novels. In fact, if one reads Northanger Abbey, one can see that Austen has a certain degree of contempt for Romantic writing, which she considers silly and hyperbolic. Instead, she is a writer whose style and narrative interventions elevate reason and self-restraint in opposition to untrammeled expression of emotion.
Perhaps the most Romantic figure in the novel is Wickham, but rather than turning out to be a hero, he is a villain. Lydia, the impulsive sister whose acts bear the greatest resemblance to romantic love on the surface, is a self-centered, spoiled teenager. On the other hand, while Austen condemns impulsiveness and extreme emotionalism, she is also not a crass pragmatist or materialist. Charlotte Lucas is a case in point. Although Elizabeth is revolted by the possibility of marrying Collins, and Austen's narrator supports that decision, the narrator is somewhat sympathetic to Charlotte's choice, not condemning it to the extent that Lydia's rash elopement is condemned, but agreeing with Charlotte's assessment of her own situation and temperament.
What Elizabeth and the narrator value in a marriage is not so much an intense romantic crush, but rather mutual respect and esteem, with husband and wife being good friends, not just passionate lovers, and being compatible in a way that lends itself to a durable life partnership. Elizabeth initially rejects Darcy out of both prejudice and pride, but accepts him when she comes to understand that he is a man of good moral character she can respect and admire and with whom she shares interests and values, something she discovers as she realizes how he is seen at Pemberly.