If I were a "tiny startup", I would absolutely leverage RDS in the first instance. Last thing I want to spend time doing is setting us Postgres and accumulating tech debt from a bad or suboptimal install. There are RDS instances that qualify for Free Tier as well if you're running _really_ lean.

In fact, the only time that I would consider migrating to a DB on EC2 is if the database isn't supported by RDS (DB2, for example, though I think there are solutions for this now), the licensing for RDS makes it cost-prohibitive or if the client needed to be able to really tweak the database engine or daemons.