Begin with relevant experience, not the length of the client list. Ask for a couple of engagements that match your stack, and then ask which is better php or python engineers actually built it. A solid partner will put you on a call with the engineers. Answers that name nobody at this stage usually mean the delivery team is not the team you were shown.
The contract deserves more scrutiny than the proposal. Three clauses do most of the work: ownership of the code, non-disclosure, and notice periods and handover. All the work product has to transfer to you once invoices are settled, along with designs, scripts and infrastructure configuration. Look closely at language that leaves so-called reusable libraries in the vendor's hands, as that is often the part you cannot replace later.
Ask how to choose a software outsourcing company they estimate. A serious estimate arrives with a written set of assumptions, a breakdown by feature or module and a range rather than a single number. A fixed price only makes sense when the requirements are stable and documented; when the scope is still moving the provider adds a risk premium and you pay for uncertainty either way. Time and materials shifts that risk to you, so it demands a cap, regular demos and transparent reporting.
Process beats the number of hire fintech developers. Find out what happens when the scope changes, who writes the acceptance criteria and how testing is organised. A mature team can walk you through a live build at the end of each sprint. Clear, written acceptance criteria stay your only real protection against the it-was-never-in-scope conversation.
Finally, think about the day you no longer need this vendor while the relationship is still good. Require that the source repository sits on infrastructure you own from the first commit, and that the documentation is refreshed in every sprint. A vendor with nothing to hide will agree quickly; resistance at this point reveals quite a lot.