I think it depends on the details and performance requirements. Otherwise the general sentiment of 'use any of the major technologies, one you're familiar with' stands.

For example, is this software aimed at the end user or will the startup use it themselves? If the end user will use it (like alerts for their portfolio/watch list), then the definition of "real-time" is going to be lax because you need human interaction. If it's used by an institution for trading, then you will need to choose highly performant language, architecture, and hardware so that your algorithm can place it's orders before other institutions. You would also likely need to integrate with Swift (financial).