I'm going to offer a few links to past answers of mine, but I'd also like to write a bit about a thing which might not be immediately apparent until you stop and think about it: There were banks in the renaissance, and then there were the Medici. The Medici were successful bankers, yes, but they were also spectacularly successful in their ability to capture the apparatus of the Florentine state and ultimately build a dynastic monarchy. So there's always a delicate balance when using the Medici as an example to stand-in for other tuscan commercial dynasties: on the one hand, some things they do aren't particularly different compared to other mercantile dynasties; on the other, there are things which they either did differently or did much more successfully compared to their peers. And to top it off, they were also helped along by a large helping of luck along the way. So while it is probable if not the Medici another dominant mercantile dynasty would have emerged at some point in Florence, the fact that it was the Medici who did emerge means that we are looking at a dynasty whose success was the exception rather than representative of the norm.

So that being said, there are a few general things to consider when thinking of the success of the Medici and other commercial dynasties:

• Reward is a function of Risk, and banking was risky business. Unlike merchants which might become highly specialized in sourcing, moving, and reselling a specific kind of good, bankers were expected to lend to a variety of commercial enterprises, including enterprises where they might not be as well-versed in as their loanees. For this risk, they charged high premiums: Loans for overseas commercial expeditions ("Sea Loans," the precursor to both naval insurance and modern trade finance, I wrote a bit about that here) for example, could carry interest of over 40%! Two prominent late 14th-century members of the Medici dynasty (Vieri di Cambio and Giovanni de Bicci) proved themselves very good at managing risk in spite of some very aggressive exposures. While this wasn't a characteristic unique to the Medici, it is what places them in the upper tier of successful Florentine bankers.

• Diversification of revenue streams. The Medici were not exclusively disbursing loans: Through the generations they participated in activities ranging from currency speculation, to managing estates, and importantly loaning money against established revenue streams (notably to the Papacy). Notably, the earliest Medici bankers (the Chiarissimi branch of the family, which would later close and whose descendants would go on to work for the da Cambio branch of the family) was contracted to manage enterprises like mints and foundries in addition to banking. While not all this activity falls under the modern definition of "Banking," they and others like them were identified as "Bankers" because no one activity represented their primary specialization: their main activity was managing money to finance enterprises undertaken by other people. Again, they were not the only ones to act in this way, but they were amongst the most successful at doing this successfully.

• Intergenerational wealth transmission. Not all wealthy merchants or bankers were successful at transmitting their wealth onto the next generation, nor were they successful in ensuring the next generation built on that wealth in the way the Medici did. Italian renaissance sources are full of testimonies (and tropes!) of miserly rich uncles leaving their fortune to a monastery or the church, and of well-to-do young men squandering the family fortune. While renaissance society was nonetheless very rigid and to some degree wealth transmission was something of upper-class and upper-middle-class families were generally able to successfully achieve, the Medici did prove themselves particularly successful in building intergenerational wealth across various branches of the family (notably in in the handoff from Vieri da Cambio to Giovanni de Bicci, where a few gard lessons might have been learned from Giovanni's father and grandfather's less-than-stellar record, as well as subsequent handoffs down to Piero until Lorenzo, who in spite of his political success squandered great part of the family fortune and who oversaw the family's banking activity quietly collapse).

And lastly, most uniquely for the Medici, they were able to translate financial power into political power. And while this political power would be the main arbiter of their legacy, it is important not to underestimate how uniquely successful their economic power was in their day, and how it was integral to their their accumulation of political power.

This answer on the early Medici bank might interest you: https://www.reddit.com/r/AskHistorians/comments/40egwc/how_did_the_house_of_medici_build_up_the_money_to/cyu4isx/

This similar answer (probably based on the one I linked above) might also interest you: https://www.reddit.com/r/AskHistorians/comments/8x7jmm/what_prevented_the_rise_of_financial_institutions/e238n5x/

This answer on studies of the medieval/renaissance banking system: https://www.reddit.com/r/AskHistorians/comments/pxlv1n/book_recommendations_on_the_intricacies_of_11th/hf4tp49/