What matters more than price
A cheap quote for the wrong thing is the most expensive option. What decides whether a project goes well is clear requirements, regular demos, a named person to talk to and access to the people actually doing the work.
A supplier that treats the project as a black box, delivering something at the end, tends to disappoint. One that keeps you in the conversation tends not to.
Questions to ask any supplier
Who will I speak to each day? Who owns the code? How is access to my systems controlled? How do you check quality? What happens if someone leaves the team?
A supplier should be able to answer all of these without hesitating.
Signs to be wary of
A price with no scope behind it. No demos until the end. Reluctance to let you talk to the developers. Vague answers about who owns what. Promises that sound too good.