I notice you left out volunteers. I'm going to suggest that often the best approach is a mix of all three. That was what I did when I worked at the Huckleberry RR.
You need paid staff to provide continuity. Bring in contractors with the specific skills you need on a given project. Your paid staff and volunteers may even learn enough to do the same job without them the next time. I can give an example - the first time we shrunk tires on I had Scott Lindsay come up. After that we were able to shrink tire on ourselves.
Another case is when you don't have a piece of equipment for a special job. We had John Bush come in and bore the cylinders on both 464 and our Ten-Wheeler. John had access to an Underwood boring bar and was familiar with it's operation.