Start with Postgres. Don't start with SQLite. SQLite is a file format, not a database; it scales atrociously (I've seen simple queries run for 10s of seconds with 100MB of data), it basically doesn't work in concurrent update scenarios, and the more data you put into it, the more pain you'll have migrating to Postgres.

Use SQLite if you want a file format where you don't want to rewrite the whole file for every update, or if you're in a situation or environment where it's not feasible to have an actual database server.