Heroku is by far the easiest and cheapest (free for light usage) way to get a Rails app into production.

Heroku‘a preference is Postgres over SQLite: https://devcenter.heroku.com/articles/sqlite3

Off the top of my head:

Postgres is a client-server system, with full user access controls and multiple client connections.

Postgres has PostGIS (geographic data) and foreign data wrappers.

Postgres is more scalable than Sqlite and can work with larger datasets over multiple instances.