From their site: https://www.sqlite.org/whentouse.html
>SQLite does not compete with client/server databases. SQLite competes with fopen().
With Postgres, you run pg_dump on the database (which is a shell one-liner, only with slightly more arguments than cp) and that's even better for putting into git because it's a text file that git can diff natively and store efficiently with delta compression.
Postgres is a fantastic database, but most of the time getting started with and using SQLite will be easier. For example -- you'd never have to secure firewall rules to a SQLite instance. Bad defaults (unlikely but possible) or some bad post-install configuration and you've got an exposed server.
I want to emphasize that my point about SQLite being viable for startups was with the assumption of a low-write high read workload -- most of the time queries won't even hit the DB but instead be served by some caching layer. It's also really easy to scale read only versions of your applications horizontally if all you've got to do is ship/swap out DB files (again at this point it might make more sense to look into a bigger DB and just scaling vertically).
The primary purpose is to replace custom (and fragile) single-file databases with something that is far more resilient and provides uniformity in implementation. The fact that it is a suprisingly good SQL database (to the point where folks are actively arguing that much more fully-fledged databases are better in some aspects) is incidental.
Postgres can run in a 256MB VPS(if one can find one these days) and has more features that you might need later.
Installing is as easy as 'apt-get install postgresql', create user, create database, done.