For a Saas maintained by one person, would you recommend MySQL or Postgres? I don’t know yet the volume of users or connections I will receive (perhaps zero?), but I do like to keep things simple (this pgbouncer thing one may need with postgres makes me feel uncomfortable).
I would use always start with Postgres, because of its vast flexibility and extremely solid feature set, not to forget the excellent docomentation. I'v used Postgres in numerous projects and never had the need for pg_bouncer. Although I am sure there are some situation where it might be beneficial to use it. E.g. on the JVM it is best practice since 20 years to always use a connection pool in front of all JDBC drivers. IMHO transactional DDL is the killer feature for a fast moving project with customers.