Not all of the cables coming out of the power supply necessarily need to be plugged in. Better to think about the other way around: think about what parts in your PC need power from the power supply. Parts that aren't getting power simply won't work, which usually means your computer won't boot up (parts won't get damaged by not being plugged in).
Do you already have a power supply you're working with? If not, you might consider buying a "fully modular" unit which doesn't have any cables coming out of the back: you plug in only the cables you need to both the component and the PSU, which is less confusing the easier to do cable management with.