Adding switch and new fixtures to basement chain lights. Why does it short?
You have a short that occurs when you turn the switch on. You do not need a 3-wire feed, just the usual 2+ground. If the short occurs only when you turn the switch I'd expect the short to be in the wiring after the switch, e.g. in a light box or in the light fixture. You should make sure your grounds are properly connected and that ground and neutral conductors are isolated from hot.

If you are not able to quickly pinpoint the problem, I'd recommend you draw out a diagram of the wiring and make sure you understand exactly what needs to be connected and how. Then go through the whole circuit and make it match. If you don't feel like you fully understand the desired layout, I'd recommend you consult an electrician or at least someone experienced with electrical work. Electrical is not super complex, but there are pitfalls where things seem functional but are not safe.