This all depends on the goals of your side project. If the goal is something other then learning how to set up infrastructure, then deploy your app on Heroku. You get most of the difficult problems dealt with and only have to focus on a couple configurations. Yes, admittedly Heroku is pricey when you start to scale up, but keep in mind that your time isn't free and that you'd need a considerable amount of traffic before it makes sense to spend a lot of time on properly setting up your app to scale.

On the other hand, if you want to learn how properly design a web application to scale, I'd suggest to get a couple boxes on DO[1]. This[2] article describes the common design for 99% of applications on the web (The last 1% is reserved for companies that have achieved enough traffic to justify hiring their own ops team). Finally, I'd suggest you read through this[3] slide deck. It goes through the steps of scaling up your application from one server to a cluster of machines.

1 - https://www.digitalocean.com/

2 - https://www.digitalocean.com/community/tutorials/5-common-se...

3 - https://speakerdeck.com/modulus/planning-for-the-horizontal-...