Start with relevant experience, not the length of the client list. Ask for a couple of projects that resemble your stack, and then find out whether those engineers are still with the igaming software development company. A solid partner will introduce you to the tech lead. Vague answers at this stage almost always mean the delivery team is not the team you were shown.
The paperwork needs a slower read than the pitch. Three clauses do most of the work: intellectual property assignment, the NDA, and exit terms and handover. Everything produced has to transfer to you on payment, together with documentation, pipelines and deployment scripts. Watch for any clause that keeps reusable components with the vendor, because that is often the part you cannot replace later.
Find out how the estimate was built. An honest estimate is accompanied by the assumptions behind it, a task-level breakdown and a best case and a worst case. A fixed price only makes sense when the scope is genuinely frozen; in any other case the provider prices the risk in and you pay for uncertainty either way. Time and materials moves the risk back to the client, so it demands a cap, regular demos and transparent reporting.
The delivery process beats headcount. Ask how a new requirement enters the plan, who writes the acceptance criteria and what the QA setup looks like. A team can show you a working build every one or software development lifecycle stages two weeks. Written acceptance criteria stay your only outsource real estate development protection against an argument at delivery time.
Finally, plan for the end of the engagement before it becomes urgent. Require that the source repository sits under your account from the beginning, and that documentation is updated as part of the work. A provider confident in its own work says yes immediately; resistance at this point says most of what you need to know.