A virtual private server (VPS) is a virtual machine hosted in a shared environment. From the developer's perspective, it would seem like a dedicated machine (hence, the word private) preloaded with an operating system. You will need to install and set up the entire stack yourself, though many VPS providers such as WebFaction and DigitalOcean offer easier Django setups.

If you are a beginner and can spare some time, I highly recommend this approach. You will be given root access, and you can build the entire stack yourself. You will not only understand how various pieces of the stack come together but also have full control in fine-tuning each individual component.

Compared to a PaaS, a VPS might work out to be more value for money, especially for high-traffic sites. You might be able to run several sites from the same server as well.