I would learn about mtbf if I were you. Everything has a failure point (generally buried deep in product info), and when you start keeping it on 24/7, the hours will burn. Those fans on your GPU will give it up way before they normally would.

Finding a used server is not a good idea either. You aren't in a data center and servers are super loud. Also, they chew up electricity like a hungry dog and his dinner.

As others have said, find a used desktop somewhere and a cheap KVM switch so you can use the same peripherals for both. It doesn't need to be beefy by any measure (maybe drive space), just affordable.