No one has mentioned Heroku yet. Starting at $7 they are a bit more expensive than DigitalOcean, but with that extra $2 you'll get their platform, their tooling for deploying the app, their database backups. Adding other services later on is also easy with their addons. By choosing Heroku you can save hundreds or thousands of dollars in ops costs over a course of a few months. The hosting cost may go up quickly, but…
Using Heroku puts two levels of bloat between you and the hardware, and locks you into a hosting environment that becomes very expensive quickly. Eschew.
Besides, not every app needs big computing power, and many businesses can thrive on Heroku for a long time. An employee of ProductHunt mentioned on a podcast that they ran their website on 3 Performance L dynos at in 2015. That's $1500 plus some extra for the database and other services they may be using (say $3k in total). That's one of the popular websites out there, and that's a pretty good indication of an upper bound of the infrastructure cost on Heroku for a popular product. Most will never exceed the $200-300 a month.
Is $3k a big sum? Yes, it's noticeable. Will you end up spending more on hosting plus the ops work that needs to be done over time for a similar app to run and grow? Likely.
EDIT: spelling