For Britain at least in that time frame it could literally have come down to what Victoria thought of the match or who she wanted to marry who.

As an example we can look at 3 royals of the time, Edward VII, Victoria's eldest son and heir, and his sons Prince Albert and the later George V.

Edward was not on the best of terms with is parents, Victoria blamed him in part for forcing Albert to his father to an early grave, and he was a bit of a playboy.

So his mother paired him with young Alexandra, daughter of the heir to the Danish crown, and whose brother would eventually be King of Greece. It was not her first pick, as the Danes were on and off at war with Prussia over the Southern lands of the country, and one of Victoria's daughters was Crown Princess of Prussia.

But she was young and of age(she was 17, he 22 when married), and of appropriate standing(high enough to marry the future King), and apparently of a moral fortitude which might do the Prince good. And it would bind another nation to Britain by marriage, she had a younger sister also who married the soon to die Russian Crown prince.

We can then fast forward a few decades to his two sons. His eldest, Albert Victor, was in many was a bigger rouge than his father ever was, in part the result of his being sent first to the Navy, then to Cambridge, where he was associate with noted Bohemians and Libertines and developed quite reputation.

Ever trying to shore up the 3rd in line to the throne, Victoria and her family settled then on Mary of Teck. Mary was a partly German royal, her father was a Duck of Teck in the German state of Wutternberg. And her upbringing was characterized by that strict Prussian hand that had been so ineffective in Edward and Albert Victor. And nicely Mary had been born and raised in Britain so she was of a familiar set and that desirable British character with some German on the side, whose mother was Victoria's cousin.

This was not the Prince's first rodeo though, he had seriously tried to get permission to marry Helene, daughter of the Orleanist Claimant to the French Throne(this being the age of the 3rd Republic after the 2nd Empire). And Victoria was even it is said to be Ok with it, so long as the Catholic/Anglican divide was accounted for by either conversion or giving up his claim. Her father though said no and that was that.

Thus Teck was sort of a compromise choice to get little Princes in the works and to the pleasure of Victoria, and to rein in the Prince.

6 weeks short of the wedding though, due to a Flue pandemic sweeping the isles the prince took ill and died in January 1892. While mourning was public and solemn, it cannot be said the stock of the crown was hurt by George becoming the new heir.

He was recalled from the Americas and a content and by accounts competent and happy career in the Royal Navy to begin to prepare for his new role. Now growing close to his brothers intended, and probably with the urging of his family, George proposed and was married to Mary in 1893. After his earlier attempt to marry his first cousin, Marie of Edinburg was shot down by the mothers.

They were married with great pageantry, and by all accounts were devoted and genuinely fond of each other, while producing heirs and accomplishing all that could be hoped for in a royal match.

An interesting source on this I actually just finished reading was 'Rules of the Game" By Andrew Gordon, nominally about British Command at Jutland it spends larger sections examining the social and personal interactions of the Royal navy in the Victorian and Edwardian eras, since many of the commanders at Jutland were very close to Royalty and others opponents, and all had interwoven careers. Hugh Evan-Thomas as the best example, commander of the 5th Battle Squadron had been good friends and confidant to George and Albert Victor from their first days as Midshipmen.