Please correct me if I'm wrong.

Banking was mostly run by Jewish communities throughout the Middle Ages simply because Christians were not allowed to put an interest on loans. Since Christianity was almost unanimous in Europe, there was little room for banking. So again, Jews were the primary loaners in Europe, if Jewish communities were 'illegal' from a certain city or town then you really had a problem. But this was usually not the case since the nobility noticed the importance of banking. The Jews in England are famous for having helped pay King Richard the Lionheart's ransom that Duke Leopold put on his head.

As for Christians banking the Templars were the first to invent the 'echeque' or check. For instance, if someone wanted to go on a crusade, they could walk down to the Templar office in Venice. They would put down some money and receive a letter of credit in a parchment roll. They would arrive in Acre on the beaches of Palestine and exchange this letter for their money, with absolutely no penalty. The Templars were a very rich military order that received special tax money from the Pope and also found itself covered in gold from donations. They were also spread out across the whole Mediterranean, this was the catalyst for banking.

Sources: Schooling I will add more later (on mobile) when I am home.

By the way, crusades are awesome.