A VPS (Virtual Private Server) is a VM (virtual machine) which is typically hosted in a cloud datacentre somewhere. Popular providers include Linode, DigitalOcean, AWS, and so on.
We are looking to create only a handful of services and most of these providers minimal VPS configurations will suffice for our requirements.
For example the $5 per month offerings from both Linode and DigitalOcean will be adequate.
Is it really self-hosting running your services on someones elses cloud computer? I say yes, because I have root to the VM but if you're a little more security or privacy focused then maybe an on-premise solution like a Raspberry Pi might suit you a little better.