I'm in college (i.e., I don't pay for electricity). I want to host side projects (my own k8s cluster, random apps, random websites, etc.). Should I buy an old desktop [0], or should I rent a VPS?

[0] https://www.ebay.com/itm/256542663644

It depends on what you're aiming to learn. If you're interested in handling hardware and connectivity, hardware is your best bet. If you want to focus on programming, the VPS is likely your best option. They're relatively affordable, and you can learn how to host a project using one, allowing you to focus on programming.

I’d avoid the hardware. It’ll just slow you down or become a distraction… not to mention that everything takes longer. Want to wipe a VPS and start over? A few clicks. Want to take an image of the system? A few clicks. With your own hardware you’ll waste an hour just trying to get the dynamic IP software working, only to find later that certain ports are blocked by your ISP. Just no.

Buying and maintaining your own equipment is a good learning experience in itself. But universities generally don't like it when you host things on their networks, so that should be considered as well.