As another user suggested, if you're new to this, consider an old PC instead of a hosted VPS. In either case, if you want to explore self-hosting, the Sky's the limit. You could do as little as a local storage/file server, all the way up to your own virtual cloud.

For example, I run (on a pair of HP EliteDesk mini-pcs)- Jellyfin media server, Logitech Media server (squeezeserver), Homeassistant, Piwigo, phpipam, Zabbix, and a couple of other things. I also use it as a lab, so any time I want to experiment, I can just spin up a VM and mess around.

If you spend some time in this sub, you'll find more than enough project ideas to keep you busy. Depending on your current skill level, you might find r/linuxupskillschallenge helpful.

Have fun!

This is what I normally recommend as well. Much more flexible, totally under your own control (for better or worse), and cheaper in the long run.

Can you clarify your terms? Unless I'm mistaken, VPS is a Virtual Private Server (instead of a dedicated bare-metal machine). KVM (Kernel Virtualized Machine) is one kind of VPS. Hyper-V, OpenVZ, XEN are other VPS types. Each have benefits and suited for different circumstances.

IIRC, OpenVZ are usually the cheapest, as they are containers, so a host can run more of them. KVM are more like a full-fledged Linux-kernel OS.