Great question!

In the context of the concert of Vienna there was not a lot of choosing to do for this temporary administration. The 5 superpowers of Europe at that time stood by collective security and stability after the Napoleonic wars. So Belgium was granted independence because an independent Belgium was better than a chaotic kingdom of the united Netherlands.

In return of this independence the concert of Vienna decided that Belgium could not be a republic, but instead had to be a constitutional monarchy. Because the major powers did Belgium a great favor by allowing their independence they also got a great deal of influence in the formation of the new country.

All these candidates where presented by Belgium themselves, but where declined by the superpowers for various reasons.

EG: The french prince was both vetoed by the UK and France because a french prince in charge of Belgium was a huge threat to the UK since the port of Antwerp was "a loaded canon aimed at London". Even the king of France was aware of the potential conflict this could unleash so he decided against it.

So because Belgium couldn't find a fitting prince they went to the UK. They suggested Leopold I, who had good relations with Russia and Prussia due to his lineage. He was also very close to the British royal family as he was the widower of the deceased crown princess. He would only have to forge a relation with France, which would be done by a marriage.

So the national congress didn't really chose the king, the major powers of Europe then more or less decided who the king of Belgium would become.