Get an architect to help you out. Digital Ocean can offer load balancing (balance load over multiple machines), you just have to install HAProxy yourself on a machine. They don't offer autoscaling (adding extra machines in case of heavy traffic)
Heroku offers a lot (no autoscaling though), it just becomes pricey at some point. However, you can only move from Heroku to let's say your own hosting on Amazon with their autoscaling when you can afford to pay at least 2 devops guys (let's say at least $15,000/month). Just one is not enough, you will need 24x7 devops.
I used to work with Tapjoy, they had 200 Amazon EC2 instances running Ruby on Rails. No need to go to your own hardware, that is very expensive an requires a lot of capital up front.
btw scalability problems are luxury problems: most companies have a product/business company and never get to the level of traffic that causes scalability problems