Hawk Host web hosting has VPS hosting servers for $18.00 per month which should cover your website for awhile.
You'll need to know how to manage a vps server though and install and configure software and stuff that your website needs.
It's more advanced to run a vps server than it is to host on shared hosting. So make sure you learn about VPS server management before diving into VPS Hosting.
There are managed vps hosting servers but you need to pay more.
https://www.hawkhost.com/vps-hosting