Begin with domain experience, not the length of the client list. Request three or four case studies that match your technology stack, and then find out whether those engineers are still with the web development company moscow. An honest provider will introduce you to the tech lead. Evasive answers at this stage almost always mean you are talking to a reseller.
The agreement warrants more scrutiny than the proposal. Three clauses do most of the work: ownership of the code, non-disclosure, and termination and handover. Every artifact has to transfer to you on payment, including documentation, pipelines and deployment scripts. Look closely at wording that keeps framework code outside the transfer, because this is frequently the dependency that makes switching painful.
Find out how the estimate was built. An honest estimate is accompanied by a list of assumptions, a task-level breakdown and a best case and a worst case. A fixed-bid deal is only reasonable when the scope is genuinely frozen; otherwise the provider pads the number and you fund the buffer regardless. Hourly billing shifts that risk to you, so it outsourcing company needs a cap, regular demos and transparent reporting.
How the work is run beats headcount. Establish what happens when the scope changes, who signs off on a feature and how testing is organised. A team can show you a live build at the end of each sprint. Acceptance criteria in writing stay the practical protection against the it-was-never-in-scope conversation.
Last, think about the day you no longer need this vendor at the start rather than at the end. Require that the repository lives on infrastructure you own from day one, and that the documentation is refreshed in every sprint. A vendor with nothing to hide accepts it without argument; resistance at this point reveals a great deal.