I'm from an Oracle background so PostgreSQL has generally been my choice. The truth is MySQL has come a long way and there is no real winner between the two. It basically comes down to preference, hosting choice and system experience.
Since you specifically said you were building a web app you might consider PG since the goal might be to close the software later on and PG will port to Oracle better. Meanwhile MySQL seems to be getting farther away from SQL. Additionally if compliance is what you are looking for then PG is what you want while MySQL seems more suited to a open source environment.
...turns out that my two cents is worth less or more depending on the current exchange rate.
roy darling *my posts seem a lot shorter in my head