In general, the people who rise to the top of social hierarchies are ones who already had a substantial degree of political, military, economic, or cultural power beforehand. This is just as true for Donald Trump and Kylie Jenner today as it was for the Árpád (Hungarian) and Piast (Polish) dynasties in the eighth and ninth centuries.

In Poland, the first king, Mieszko I, allegedly founded the Piast dynasty in 965 when he married Dobrava, daughter of Duke Boleslav I of Bohemia. He and the subsequent rulers of the Piast dynasty were glad to forge diplomatic marriages with German, Scandinavian, Hungarian, and Rus' royalty/leadership, which gave them sufficient recognition, sovereignty, and military support from most of their neighbors to establish themselves as rulers of the Regnum Poloniae.

Mieszko also converted to the faith of his neighbors, the Bohemians (Latin Christianity), which further endeared him to his Czech and German allies. Although the Poles as a group did not accept Christianity until the 1100-1200s, the Piast adoption of Latin Christianity in the late 900s earned them enough political capital from the Czechs and the Germans to maintain control of Poland. According to Lukowski and Zawadzki, “the Church remained an alien, unpopular institution, foisted on the people by a ruling elite in pursuit of its own political and expansionist ambitions.”

The Poles also paid tribute to the very powerful Holy Roman Empire in the form of money and levied warriors in exchange for sovereignty over the Polish plains and marches. According to the merchant Ibrahim ibn Yakub, Mieszko I had a 3,000-person standing army, which was apparently large enough to go toe-to-toe with the geographically-much-larger HRE if necessary. Mieszko used his military might to annex Silesia from his Bohemian in-laws, and apparently founded the important port city of Gdansk to consolidate power over the river mouth where it sits. Mieszko's son, Bolesław I, gave his sister in marriage to the ruler of the Grand Duchy of Kiev and intervened substantially in Kiev's politics to keep power there, which provided stability and allies on his eastern borders.

Jumping over to Hungary, the Magyars first arrived in the Pannonian Basin between 850-900 CE, but the first king (St. Stephen I of the Árpád dynasty) did not crown himself until 1000 CE. The Árpád family was the most powerful in Hungary for one reason: they controlled the Danube River.

The early Hungarian dynasty had a substantial, if antagonistic, relationship with its neighbors, the Roman (Byzantine) Empire and the Bulgarian Empire (both Orthodox). Prince Géza converted to Latin Christianity in the 980s just to spite Byzantium, and thus began a top-down Christianization of Hungary. Molnár describes Géza's Christianization as “more violent than pious.” He forced lords to convert and persecuted “shamans and pagans.” Because of the choice of Latin Christianity, the first king of Hungary, Stephen I Árpád, earned the social and military support of Holy Roman Emperors Otto I, II, and III.

In St. Stephen's case, three more ways he centralized and consolidated power were: he promulgated the first code of laws, established rules of private property, divided Hungary into 40 counties (comitatus), and appointed a governor (ispán) for each one. By “modernizing” the Hungarian state in this way and appointing lords of his choice to administer the political units, Stephen ensured his reign was stable, peaceful, and productive.

TL;DR: if you want to rule or get very rich, you need to have or seem to have more political, military, financial, or social power than your competitors. Sometimes this means you convert to Latin Christianity just to spite Byzantium, and sometimes you marry your sister to the Grand Prince of Kiev. It helps if you start out controlling the Danube River.

Sources:

The Cambridge Concise History of Hungary by Miklós Molnár, translated by Anna Magyar. 2001.

The Cambridge Concise History of Poland by Jerzy Łukowski and Hubert Zawadzki. Third Edition, 2019.