>But if you want to also consider how cheap you can run your app, you need to consider how many app servers will it take to saturate the DB?
Moore's law has made this sorta moot. Unless you're on Heroku, for a successful small-to-medium app, the denominator in your hosting costs is doing to be the salary of the engineer or sysadmin who tends to it.
(If you're on Heroku, then you start worrying about dynos because, with monitoring, you're paying $60 per "worker".)
This is to say, the cost in salary to properly shard a database probably outweighs a year or two of hosting for the extra two or three boxes you're spinning up; almost no one experiences explosive growth where you need to spin up dozens of new boxes overnight.