Newbie who knows nothing!

Illustrator would be better. Photoshop can handle paths to create shapes but it's by no means as good as Illustrator for creating precise shapes.
Best method for creating the swirl would surely be the 3D tool in Illy (also availbable in photoshop if you did decide to do a raster version). There are stacks of variables to play about with until you get what you're after. Others might suggest creating something like that in a 3D program, (if you have the oppurtunity) and importing it, but again, it won't be vector.