The first four Georges had to marry Protestants to keep Great Britain and had to marry daughters of rulers (petty or great) to keep Hanover. Hanover gave them a small independent income, an army they could deploy at will, and somewhere to go if the exiled Stuarts drove them out. There were reasons why they didn't and/or couldn’t intermarry with Swedish and Danish royals which I will reserve for reasons of space, so German royals were the only game in town for a long, long, time.
Caroline of Ansbach was chosen as George II’s bride because she was the Protestant daughter of a ruler and because she was lovely, healthy, smart as a whip, and too well-bred to emulate his mother's deplorable hijinks. The Hanoverians realized that George needed a loving, decisive, and tactful wife; they could have looked higher for a bride for him, but they realized that she was the perfect choice. She had other options: Archduke Charles, later Emperor Charles VI, wanted to marry her, but she didn’t want to become a Catholic.
The wives of Frederick, Prince of Wales, George III, and George IV were not chosen so thoughtfully. Frederick’s wife was chosen in a hurry because it was believed that he might run away and marry Lady Diana Spencer (a granddaughter of Sarah Churchill, Dowager Duchess of Marlborough) who was dynastically unsuitable. George III’s bride was chosen by his mother, who was not one of the great thinkers of her own, or any other, time. George IV was forced to marry in a hurry so that he could have his debts paid. He was given a choice between a niece of his father and a niece of his mother; he didn’t want either, for he was madly in love with Maria Fitzherbert, whom he had secretly (but illegally) married. He chose Caroline of Brunswick in haste and repented at leisure.
If you're looking for a good book about Lady Sarah Lennox, you should read Dinah Lampitt's novel about her, As Shadows Haunting. It's not a traditional historical novel; there's time travel involved as well as a parallel story, but it's fairly well researched and is a lot more engaging than Tillyard's biography.