As an answer to the questions about collecting dust, shavings, and debris at the lathe, I offer the following:
Forget about the large shavings. They are a clean-up problem, not a health problem.
Regardless of its size, there isn't a home-shop dust collector made that will move enough air to pick up enough of the shavings and debris to do any good.
Dust is a health problem. I will tell anyone who wants to argue this point to come back in 20-years and tell me again that it isn't.
A Shop-Vac doesn't move enough air to be of any value.
Any dust collector with a 4" suction hose and at least 700 CFM capacity will do a reasonable job of picking up the airborne dust.
The only question remaining is how we use it. My solution is shown in the following photographs.
I started with a packing box so I could cut and fit while I tried to find a way to install a more permanent collection hood that would still give me access for turning and sanding. In the end, the permanent solution was to find a better box. If I want a larger hood, I get a bigger box.
The base is a piece of ½" plywood that is stuck between the ways of the lathe. The box came from the local liquor store because theirs are heavier than other packing boxes. The suction hose is stuck into a tight-fitting hole in the bottom of the box and the corrugations and a piece of duct tape keep it from falling out. The box is held on the base with two spring-clamps, which makes its location adjustable. I left the top flaps in because they give some stiffness to the box, and they can be used as deflectors to direct the air flow.