If I were buying an app, I'd be happy with MySQL or MS SQL Server, assuming appropriate hosting.
And by "assuming appropriate hosting," I mean that MS SQL Server is a great product and I like it a lot, but Windows-based hosting is more expensive than Linux-based, and thus I'd only go with Windows-based hosting if there were a reason to (e.g. my app was written in ASP.NET) -- I wouldn't pay the extra for Windows hosting just to use MS SQL.
PostgreSQL is a fine product, but there's very little reason to choose it over the ubiquitous MySQL.
SQLite isn't a "real" database; I consider SQLite an alternative to flat files, not an alternative to an RDBMS. The performance just isn't there on large datastores. Which isn't to say I don't use it -- just that I don't use it for anything complex enough to involve JOINs on more than two tables.